For a bounded operator T acting on an infinite dimensional separable Hilbert space H, we prove the following assertions： （i） If T or T＊ ∈ SC, then generalized a- Browder＇s theorem holds for f（T） for every f ∈...For a bounded operator T acting on an infinite dimensional separable Hilbert space H, we prove the following assertions： （i） If T or T＊ ∈ SC, then generalized a- Browder＇s theorem holds for f（T） for every f ∈ Hol（σ（T））. （ii） If T or T＊ ∈ HC has topological uniform descent at all λ ∈ iso（a（T））, then generalized Weyl＇s theorem holds for f（T） for every f ∈ Hol（σ（T））. （iii） If T ∈ HC has topological uniform descent at all λ ∈（T）, then T satisfies generalized Weyl＇s theorem. （iv） Let T ∈ HC. If T satisfies the growth condition Gd（d 〉 1）, then generalized Weyl＇s theorem holds for f（T） for every f ∈ Hol（σ（T））. （v） If T ∈ SC, then, f（OssF＋ （T）） = aSBF＋ （f（T）） for all f ∈ Hol（σ（T））. （vi） Let T be a-isoloid such that T＊ ∈ HC. If T - AI has finite ascent at every A ∈ Eσ（T） and if F is of finite rank on Hsuch that TF = FT, then T ∈ F obeys generalized a-Weyl＇s theorem.展开更多
Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special ...Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, KSthe （LF）-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems.展开更多
A Banach space operator satisfies generalized RakoSevi5＇s property （gw） if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the...A Banach space operator satisfies generalized RakoSevi5＇s property （gw） if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the spectrum of T. In this note, we characterize hypecyclic and supercyclic operators satisfying the property （gw）.展开更多
Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L...Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L ： B（X） →B（X） to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied＇ by Chan and here we obtain an analogous result in the case of ＊-strong operator topology.展开更多
We denote N, R, C the sets of natural, real and complex numbers respectively. Let (λ<sub>n</sub>), n ∈ N be an unbounded sequence of complex numbers. Costakis has proved the following result. There ...We denote N, R, C the sets of natural, real and complex numbers respectively. Let (λ<sub>n</sub>), n ∈ N be an unbounded sequence of complex numbers. Costakis has proved the following result. There exists an entire function f with the following property: for every x, y ∈ R with 0 , every θ ∈(0,1) and every a ∈ C there is a subsequence of natural numbers (m<sub>n</sub>), n ∈ N such that, for every compact subset L ⊆C , In the present paper we show that the constant function a cannot be replaced by any non-constant entire function G. This is so even if one demands the convergence in (*) only for a single radius r and a single positive number θ. This result is related with the problem of existence of common universal vectors for an uncountable family of sequences of translation operators.展开更多
Let G be a locally compact group, and let 1≤p〈∞. We characterize topolog- ically multiply recurrent weighted translation operators on LP（G） in terms of the Haax mea- sure and the weight function. We also show tha...Let G be a locally compact group, and let 1≤p〈∞. We characterize topolog- ically multiply recurrent weighted translation operators on LP（G） in terms of the Haax mea- sure and the weight function. We also show that there do not exist any recurrent weighted translation operators on L^∞ （G）.展开更多
In this paper. we stady the nonwandering operator, which is a linear operator with chaos character and is in intnite dimensionol linear space. We give the hypercyclic bacomposition on the compact set of nonwandering o...In this paper. we stady the nonwandering operator, which is a linear operator with chaos character and is in intnite dimensionol linear space. We give the hypercyclic bacomposition on the compact set of nonwandering operators.展开更多
So far there is a lack of specialized research on the entire path and the law of the evolution of green economy modes,especially studies on its future trend.Some studies have been done only on its sub-process,in which...So far there is a lack of specialized research on the entire path and the law of the evolution of green economy modes,especially studies on its future trend.Some studies have been done only on its sub-process,in which there are some shortcomings such as overlapping and incomplete classification of economy modes,as well as the lack of mechanism models to describe the modes.This paper attempts to solve those problems.Firstly,various green economy modes are extracted and classified,and then their evolution paths are identified and reviewed,according to sustainable development theory,hypercycle theory,etc.,and to practical investigation.Secondly,theoretical models for each green economy mode and their multilevel dynamic evolution models in a practical field(forestry as an example)are established by the modeling method of system structure.Finally,the evolution law of green economy mode is analyzed systematically by means of the above-mentioned models.According to the research,some conclusions are drawn as follows:First,green economy modes have evolved through three stages as a whole.The first is the start-up stage,in which the mode is the‘from cradle to grave’end-treatment green economy(GE-I).The second is the growth stage,in which the mode is the‘from cradle to cradle’resources-chain closed-loop green economy(GE-Ⅱ).The third is the mature stage,in which the mode will be the‘from breeding to breeding‘three-chain hypercycle economy(GE-Ⅲ).Second,GEⅡhas evolved through a specific process.In depth,the basic framework of GEⅡis based on the circular economy theory;and then it is combined gradually with some other relevant theories and technologies that are cleaner production,low-carbon economy and sharing economy and so on.In breadth,GE-Ⅱis expanded layer by layer from unified enterprise GE-Ⅱto diversified enterprise(or cluster)GE-Ⅱ,and to societal GE-Ⅱ.The operational principle of GE-Ⅱcan be described by 3R theoretical model that includes 3 subsystems of reduction,recycle and reuse(3R),which are connected into an organic whole by resources chain.Third,GE-Ⅲis evolving through a specific process of three-chain(3C)stage by stage expansion,from resources-chain primary hypercycle to eco-chain secondary hypercycle,and to value-chain tertiary hypercycle.The operational principle of GE-Ⅲcan be described by 5R-3C theoretical model that includes 5 subsystems of reduction,recycle,reuse,recultivation and reallocation(5R),which are connected into an environment-economy self organizing system by resources chain,ecochain and value chain.In the system,resources chain is the foundation,eco-chain is the support,and value chain is the impetus.The 3C hypercycle promotes and catalyze each other to realize mutualism between ecosystem and industrial system.Fourth,the related field of GEⅢincludes the principal part of renewable-resource-based industry,and the expanded part of other relevant industries and even the whole society.Now in practice,GE-Ⅲhas initially formed.And in the future,it is the development tendency of green economy toward the establishment of the ecological civilization.展开更多
By the new spectrum originated from the single-valued extension property,we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω)holds.Meanwhile,th...By the new spectrum originated from the single-valued extension property,we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω)holds.Meanwhile,the relationship between hypercyclic property(or supercyclic property)and property(ω)is discussed.展开更多
A subgroup E of a finite group G is called hypercyclically embedded in G if every chief factor of G below E is cyclic.Let A be a subgroup of a group G.Then we call any chief factor H/AG of G a G-boundary factor of A.F...A subgroup E of a finite group G is called hypercyclically embedded in G if every chief factor of G below E is cyclic.Let A be a subgroup of a group G.Then we call any chief factor H/AG of G a G-boundary factor of A.For any G-boundary factor H/AG of A,we call the subgroup(A∩H)/AG of G/AG a G-trace of A.On the basis of these notions,we give some new characterizations of hypercyclically embedded subgroups.展开更多
In this paper,we introduce and study the diskcyclicity and disk transitivity of a set of operators.We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity.As appli...In this paper,we introduce and study the diskcyclicity and disk transitivity of a set of operators.We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity.As applications,we study the diskcyclicty of Co-semigroups and C-regularized groups.We show that a diskcyclic Co-semigroup exists on a complex topological vector space X if and only if dim(X)=1 or dim(X)=∞and we prove that diskcyclicity and disk transitivity of C0-semigroups(resp C-regularized groups)are equivalent.展开更多
Let X be a separable infinite dimensional Banach space and B（X） denote its operator algebra, the algebra of all bounded linear operators T ： X → X. Define a left multiplication mapping LT ： B（X）→B（X） by LT（...Let X be a separable infinite dimensional Banach space and B（X） denote its operator algebra, the algebra of all bounded linear operators T ： X → X. Define a left multiplication mapping LT ： B（X）→B（X） by LT（V） → TV, V ∈ B（X）. We investigate the connections between hypercyclic and chaotic behaviors of the left multiplication mapping LT on S（Z） and that of operator T on X. We obtain that LT is SOT-hypercyclic if and only if T satisfies the Hypercyclicity Criterion. If we define chaos on B（X） as SOT-hypercyclicity plus SOT-dense subset of periodic points, we also get that LT is chaotic if and only if T is chaotic in the sense of Devaney.展开更多
文摘For a bounded operator T acting on an infinite dimensional separable Hilbert space H, we prove the following assertions： （i） If T or T＊ ∈ SC, then generalized a- Browder＇s theorem holds for f（T） for every f ∈ Hol（σ（T））. （ii） If T or T＊ ∈ HC has topological uniform descent at all λ ∈ iso（a（T））, then generalized Weyl＇s theorem holds for f（T） for every f ∈ Hol（σ（T））. （iii） If T ∈ HC has topological uniform descent at all λ ∈（T）, then T satisfies generalized Weyl＇s theorem. （iv） Let T ∈ HC. If T satisfies the growth condition Gd（d 〉 1）, then generalized Weyl＇s theorem holds for f（T） for every f ∈ Hol（σ（T））. （v） If T ∈ SC, then, f（OssF＋ （T）） = aSBF＋ （f（T）） for all f ∈ Hol（σ（T））. （vi） Let T be a-isoloid such that T＊ ∈ HC. If T - AI has finite ascent at every A ∈ Eσ（T） and if F is of finite rank on Hsuch that TF = FT, then T ∈ F obeys generalized a-Weyl＇s theorem.
基金Supported by the National Natural Science Foundation of China(10571035,10871141)
文摘Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, KSthe （LF）-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems.
文摘A Banach space operator satisfies generalized RakoSevi5＇s property （gw） if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the spectrum of T. In this note, we characterize hypecyclic and supercyclic operators satisfying the property （gw）.
文摘Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L ： B（X） →B（X） to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied＇ by Chan and here we obtain an analogous result in the case of ＊-strong operator topology.
基金supported in part by the Foundation of Henan Educational Committee(18A110023)the Scientific Research Foundation for Ph.D.of Henan Normal University(No.qd16151)
文摘This paper characterizes some sufficient and necessary conditions for the hypercyclicity of multiples of composition operators on Hlog,0∞.
文摘We denote N, R, C the sets of natural, real and complex numbers respectively. Let (λ<sub>n</sub>), n ∈ N be an unbounded sequence of complex numbers. Costakis has proved the following result. There exists an entire function f with the following property: for every x, y ∈ R with 0 , every θ ∈(0,1) and every a ∈ C there is a subsequence of natural numbers (m<sub>n</sub>), n ∈ N such that, for every compact subset L ⊆C , In the present paper we show that the constant function a cannot be replaced by any non-constant entire function G. This is so even if one demands the convergence in (*) only for a single radius r and a single positive number θ. This result is related with the problem of existence of common universal vectors for an uncountable family of sequences of translation operators.
基金supported by MOST of Taiwan(MOST104-2115-M-142-002-)
文摘Let G be a locally compact group, and let 1≤p〈∞. We characterize topolog- ically multiply recurrent weighted translation operators on LP（G） in terms of the Haax mea- sure and the weight function. We also show that there do not exist any recurrent weighted translation operators on L^∞ （G）.
文摘In this paper. we stady the nonwandering operator, which is a linear operator with chaos character and is in intnite dimensionol linear space. We give the hypercyclic bacomposition on the compact set of nonwandering operators.
文摘So far there is a lack of specialized research on the entire path and the law of the evolution of green economy modes,especially studies on its future trend.Some studies have been done only on its sub-process,in which there are some shortcomings such as overlapping and incomplete classification of economy modes,as well as the lack of mechanism models to describe the modes.This paper attempts to solve those problems.Firstly,various green economy modes are extracted and classified,and then their evolution paths are identified and reviewed,according to sustainable development theory,hypercycle theory,etc.,and to practical investigation.Secondly,theoretical models for each green economy mode and their multilevel dynamic evolution models in a practical field(forestry as an example)are established by the modeling method of system structure.Finally,the evolution law of green economy mode is analyzed systematically by means of the above-mentioned models.According to the research,some conclusions are drawn as follows:First,green economy modes have evolved through three stages as a whole.The first is the start-up stage,in which the mode is the‘from cradle to grave’end-treatment green economy(GE-I).The second is the growth stage,in which the mode is the‘from cradle to cradle’resources-chain closed-loop green economy(GE-Ⅱ).The third is the mature stage,in which the mode will be the‘from breeding to breeding‘three-chain hypercycle economy(GE-Ⅲ).Second,GEⅡhas evolved through a specific process.In depth,the basic framework of GEⅡis based on the circular economy theory;and then it is combined gradually with some other relevant theories and technologies that are cleaner production,low-carbon economy and sharing economy and so on.In breadth,GE-Ⅱis expanded layer by layer from unified enterprise GE-Ⅱto diversified enterprise(or cluster)GE-Ⅱ,and to societal GE-Ⅱ.The operational principle of GE-Ⅱcan be described by 3R theoretical model that includes 3 subsystems of reduction,recycle and reuse(3R),which are connected into an organic whole by resources chain.Third,GE-Ⅲis evolving through a specific process of three-chain(3C)stage by stage expansion,from resources-chain primary hypercycle to eco-chain secondary hypercycle,and to value-chain tertiary hypercycle.The operational principle of GE-Ⅲcan be described by 5R-3C theoretical model that includes 5 subsystems of reduction,recycle,reuse,recultivation and reallocation(5R),which are connected into an environment-economy self organizing system by resources chain,ecochain and value chain.In the system,resources chain is the foundation,eco-chain is the support,and value chain is the impetus.The 3C hypercycle promotes and catalyze each other to realize mutualism between ecosystem and industrial system.Fourth,the related field of GEⅢincludes the principal part of renewable-resource-based industry,and the expanded part of other relevant industries and even the whole society.Now in practice,GE-Ⅲhas initially formed.And in the future,it is the development tendency of green economy toward the establishment of the ecological civilization.
基金Supported by the National Natural Science Foundation of China(Grant No.111501419)the Doctoral Fund of Shaanxi province of China(Grant No.2017BSHEDZZ108)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2021JM-519)。
文摘By the new spectrum originated from the single-valued extension property,we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω)holds.Meanwhile,the relationship between hypercyclic property(or supercyclic property)and property(ω)is discussed.
基金Research of the first author is supported by aNNSFgrant ofChina(Grant#11371335)WuWen-Tsun Key Laboratory of Mathematics,USTC,Chinese Academy of Sciences.Research of the second author supported by Chinese Academy of Sciences Visiting Professorship for Senior International Scientists(Grant No.2010T2J12).
文摘A subgroup E of a finite group G is called hypercyclically embedded in G if every chief factor of G below E is cyclic.Let A be a subgroup of a group G.Then we call any chief factor H/AG of G a G-boundary factor of A.For any G-boundary factor H/AG of A,we call the subgroup(A∩H)/AG of G/AG a G-trace of A.On the basis of these notions,we give some new characterizations of hypercyclically embedded subgroups.
文摘In this paper,we introduce and study the diskcyclicity and disk transitivity of a set of operators.We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity.As applications,we study the diskcyclicty of Co-semigroups and C-regularized groups.We show that a diskcyclic Co-semigroup exists on a complex topological vector space X if and only if dim(X)=1 or dim(X)=∞and we prove that diskcyclicity and disk transitivity of C0-semigroups(resp C-regularized groups)are equivalent.
基金Supported by the Science Foundation of Department of Education of Anhui Province (Grant No. KJ2008B249)the Foundation of Hefei University (Grant No. RC039)
文摘Let X be a separable infinite dimensional Banach space and B（X） denote its operator algebra, the algebra of all bounded linear operators T ： X → X. Define a left multiplication mapping LT ： B（X）→B（X） by LT（V） → TV, V ∈ B（X）. We investigate the connections between hypercyclic and chaotic behaviors of the left multiplication mapping LT on S（Z） and that of operator T on X. We obtain that LT is SOT-hypercyclic if and only if T satisfies the Hypercyclicity Criterion. If we define chaos on B（X） as SOT-hypercyclicity plus SOT-dense subset of periodic points, we also get that LT is chaotic if and only if T is chaotic in the sense of Devaney.
