In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
文章主要研究Banach代数上反三角算子矩阵的Hirano逆.假设a∈A^(H),b∈A^(sD).如果b^(D)a=0,bab^(π)=0,证明了[a 1 b 0]具有Hirano逆,进而研究了反三角算子矩阵在弱交换条件下的Hirano逆.由此获得了新的可以分解为三幂等元与幂零元和...文章主要研究Banach代数上反三角算子矩阵的Hirano逆.假设a∈A^(H),b∈A^(sD).如果b^(D)a=0,bab^(π)=0,证明了[a 1 b 0]具有Hirano逆,进而研究了反三角算子矩阵在弱交换条件下的Hirano逆.由此获得了新的可以分解为三幂等元与幂零元和的算子矩阵.展开更多
The invariant determinants ha Banach algebras are discussed and a necessary and sufficient condition for those integral traced unital Barach algebra(A,τ) admitting a G-invari- ant determinant is obtained,where G is a...The invariant determinants ha Banach algebras are discussed and a necessary and sufficient condition for those integral traced unital Barach algebra(A,τ) admitting a G-invari- ant determinant is obtained,where G is a group of trace preserving automorphisms of A.展开更多
Let a, b be two generalized Drazin invertible elements in a Banach algebra. An explicit expression for the generalized Drazin inverse of the sum a + b in terms of a,b,a^d,b^d is given. The generalized Drazin inverse f...Let a, b be two generalized Drazin invertible elements in a Banach algebra. An explicit expression for the generalized Drazin inverse of the sum a + b in terms of a,b,a^d,b^d is given. The generalized Drazin inverse for the sum of two elements in a Banach algebra is studied by means of the system of idempotents. It is first proved that a + b∈A^(qnil) under the condition that a,b∈A^(qnil),aba = 0 and ab^2= 0 and then the explicit expressions for the generalized Drazin inverse of the sum a + b under some newconditions are given. Also, some known results are extended.展开更多
The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of ...The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability (briefly, HUR-stability) originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.展开更多
For a Banach algebra A, we denote by .A* and .A** the first and the second duals of A respectively. Let T be a mapping from .A* to itself. In this article, we will investigate some stability results concerning the...For a Banach algebra A, we denote by .A* and .A** the first and the second duals of A respectively. Let T be a mapping from .A* to itself. In this article, we will investigate some stability results concerning the equations T(αf + βg) -= αT(f) + βT(g), T(af) = aT(f) andT(αf +βg) + T(αf - βg) =- 2α2T(f) + 2β2T(g) where f, g e .A*, a ∈ A, and α,β ∈ Q / {0}.展开更多
In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generaliz...In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generalize some results in the literature. Moreover,we give an example to support the main assertions.展开更多
In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theore...In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r(λ) of the g-quasi-contractive constant vector λ satisfying r(λ) ∈[0,1) in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.展开更多
We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result...We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.展开更多
The purpose of this paper is to improve some famous theorems for contractive mapping from ρ(α + β) ∈ [0,1/s) to ρ(α + β) ∈ [0, 1) in ordered cone b-metric spaces over Banach algebras with coefficient s ≥ 1(ρ...The purpose of this paper is to improve some famous theorems for contractive mapping from ρ(α + β) ∈ [0,1/s) to ρ(α + β) ∈ [0, 1) in ordered cone b-metric spaces over Banach algebras with coefficient s ≥ 1(ρ(x) is the spectral radius of the generalized Lipschitz constant x). Moreover, some similar improvements in ordered cone b-metric spaces are also obtained, which from α + β∈ [0,1/s) to α + β∈ [0, 1). Some examples are given to support that our new results are genuine improvements and generalizations.展开更多
Let V1 and V2 be two -Banach algebras and Ri be the right operator Banach algebra and Li be the left operator Banach algebra of Vi(i=1,2). We give a characterization of the Jacobson radical for the projective tensor p...Let V1 and V2 be two -Banach algebras and Ri be the right operator Banach algebra and Li be the left operator Banach algebra of Vi(i=1,2). We give a characterization of the Jacobson radical for the projective tensor product V1rV2 in terms of the Jacobson radical for R1rL2. If V1 and V2 are isomorphic, then we show that this characterization can also be given in terms of the Jacobson radical for R2rL1.展开更多
In this paper, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contain various integral and functional equations that are considered in nonlinear anal...In this paper, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contain various integral and functional equations that are considered in nonlinear analysis. Our considerations will be discussed in Banach algebra using a fixed point theorem instead of using the technique of measure of noncompactness. An important special case of that functional equation is Chandrasekhar’s integral equation which appears in radiative transfer, neutron transport and the kinetic theory of gases [1].展开更多
In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the inva...In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.展开更多
In this paper,we discuss that the polynomial spectrum,relative spectrum and Spectrum of a Pair of Elements are all compact,so their resolvent sets are all open.
In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assump...In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.展开更多
The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (...The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (A) is decompcoable, moreover, in the Hilbert algebras case the assumation that A is abelian and A has an identity can be released. Those results are partially answers to a question raised by K. B. Laursen and M. M. Neumann [5].展开更多
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
文摘A determinant theory is developed for Banach algebras and a characterization of those traced unital Banach algebras admitting a determinant is given.
文摘The invariant determinants ha Banach algebras are discussed and a necessary and sufficient condition for those integral traced unital Barach algebra(A,τ) admitting a G-invari- ant determinant is obtained,where G is a group of trace preserving automorphisms of A.
基金The National Natural Science Foundation of China(No.11371089,11371165)the Natural Science Foundation of Jilin Province(No.20160101264JC)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)the Natural Science Foundation of Jiangsu Province(No.BK20141327)the Fundamental Research Funds for the Central Universities,the Foundation of Graduate Innovation Program of Jiangsu Province(No.KYZZ15-0049)
文摘Let a, b be two generalized Drazin invertible elements in a Banach algebra. An explicit expression for the generalized Drazin inverse of the sum a + b in terms of a,b,a^d,b^d is given. The generalized Drazin inverse for the sum of two elements in a Banach algebra is studied by means of the system of idempotents. It is first proved that a + b∈A^(qnil) under the condition that a,b∈A^(qnil),aba = 0 and ab^2= 0 and then the explicit expressions for the generalized Drazin inverse of the sum a + b under some newconditions are given. Also, some known results are extended.
文摘The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability (briefly, HUR-stability) originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
文摘For a Banach algebra A, we denote by .A* and .A** the first and the second duals of A respectively. Let T be a mapping from .A* to itself. In this article, we will investigate some stability results concerning the equations T(αf + βg) -= αT(f) + βT(g), T(af) = aT(f) andT(αf +βg) + T(αf - βg) =- 2α2T(f) + 2β2T(g) where f, g e .A*, a ∈ A, and α,β ∈ Q / {0}.
基金Supported by the Science and Technology Research Project of the Education Department of Hubei Province(B2015137) Supported by the National Social Science Foundation of China(12BZS050)
文摘In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generalize some results in the literature. Moreover,we give an example to support the main assertions.
基金supported by the National Natural Science Foundation of China(No.11361064)the project No.174024 of the Ministry of Education,Science and Technological Department of the Republic of Serbia
文摘In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r(λ) of the g-quasi-contractive constant vector λ satisfying r(λ) ∈[0,1) in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.
文摘We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.
基金Supported by Yunnan Applied Basic Research Projects(2016FD082)Guiding project of Scientific Research Fund of Yunnan Provincial Education Department(2016ZDX151)
文摘The purpose of this paper is to improve some famous theorems for contractive mapping from ρ(α + β) ∈ [0,1/s) to ρ(α + β) ∈ [0, 1) in ordered cone b-metric spaces over Banach algebras with coefficient s ≥ 1(ρ(x) is the spectral radius of the generalized Lipschitz constant x). Moreover, some similar improvements in ordered cone b-metric spaces are also obtained, which from α + β∈ [0,1/s) to α + β∈ [0, 1). Some examples are given to support that our new results are genuine improvements and generalizations.
文摘Let V1 and V2 be two -Banach algebras and Ri be the right operator Banach algebra and Li be the left operator Banach algebra of Vi(i=1,2). We give a characterization of the Jacobson radical for the projective tensor product V1rV2 in terms of the Jacobson radical for R1rL2. If V1 and V2 are isomorphic, then we show that this characterization can also be given in terms of the Jacobson radical for R2rL1.
文摘In this paper, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contain various integral and functional equations that are considered in nonlinear analysis. Our considerations will be discussed in Banach algebra using a fixed point theorem instead of using the technique of measure of noncompactness. An important special case of that functional equation is Chandrasekhar’s integral equation which appears in radiative transfer, neutron transport and the kinetic theory of gases [1].
文摘In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.
基金Supported by the Young Teachers Fund of North China Electric Power University(200611005)
文摘In this paper,we discuss that the polynomial spectrum,relative spectrum and Spectrum of a Pair of Elements are all compact,so their resolvent sets are all open.
基金supported by the Foundation of Education Ministry,Hubei Province,China(Q20122203)
文摘In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.
文摘The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (A) is decompcoable, moreover, in the Hilbert algebras case the assumation that A is abelian and A has an identity can be released. Those results are partially answers to a question raised by K. B. Laursen and M. M. Neumann [5].