设a、b为C-代数中的两个元,上线性映射M<sub>a.b</sub>:x→axb称为的一个乘子,而S=sum from i=1 to n M<sub>a<sub>i</sub>.b<sub>i</sub></sub>称为上的初等算子。如果M<sub>a....设a、b为C-代数中的两个元,上线性映射M<sub>a.b</sub>:x→axb称为的一个乘子,而S=sum from i=1 to n M<sub>a<sub>i</sub>.b<sub>i</sub></sub>称为上的初等算子。如果M<sub>a.a</sub>是上的紧、有限秩、一秩映射,则分别称a是中的紧元、有限维元、一维元;如果对任意x,y∈,xay=0蕴涵xa=0或ay=0,则称a为中的single元,如果C-代数中的任两个非零理想的积仍是非零的,则称是素的,近年来对于C-代数上乘子及初等算子有不少文献作了深入探讨,展开更多
This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X. First, the sufficient and necessary conditions for a local C-se...This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X. First, the sufficient and necessary conditions for a local C-semigroup and a C-cosine function to be the restriction of a global C-semigroup and a global C-cosine function to an interval are given, respectively. Secondly, it is characterized for a closed operator to be the generator of a local C-semigroup and a local C-cosine function, respectively.展开更多
in this paper, we first give a Hille-Yosida type sufficient and necessary conditionfor n-times integrated mild C-existence families. Then, we present a Laplace type sufficientand necessary condition for exponentially ...in this paper, we first give a Hille-Yosida type sufficient and necessary conditionfor n-times integrated mild C-existence families. Then, we present a Laplace type sufficientand necessary condition for exponentially bounded n-times integrated C-semigrougs, andstudy the relationship between integrated regularized semigroups and general regularizedsemigroups. Finally, we offer a characterization of integrated C-semigroups in terms of thesolvability of abstract Cauchy problems.展开更多
By defined holomorphic n-times integrated mild C-existence families and Csemigroups, their relationship with holomorphic mild C1-exustence families and holomorphic C1 -semigroups is discussed, respectively. For expone...By defined holomorphic n-times integrated mild C-existence families and Csemigroups, their relationship with holomorphic mild C1-exustence families and holomorphic C1 -semigroups is discussed, respectively. For exponentially bounded cases, this papergives several Hille-Yosida type conditions for an operator to have (or generate) one of thesefamilies of operators and generalize the corresponding results in [1], [2] and [3]. These families by the holomorphic solvability of the abstract Cauchy problem is also characterized.展开更多
Let X be a separable complex Hilbert space, B(X)the set of all (bounded linear)operators acting on X. For T∈B(X), the question whether T can be factorized into the product of some good operators has been discussed by...Let X be a separable complex Hilbert space, B(X)the set of all (bounded linear)operators acting on X. For T∈B(X), the question whether T can be factorized into the product of some good operators has been discussed by many authors (e. g. Ref. [1]—[6]). In [1], Wu obtained some sufficient and necessary conditions for an operator to be a prod-展开更多
文摘设a、b为C-代数中的两个元,上线性映射M<sub>a.b</sub>:x→axb称为的一个乘子,而S=sum from i=1 to n M<sub>a<sub>i</sub>.b<sub>i</sub></sub>称为上的初等算子。如果M<sub>a.a</sub>是上的紧、有限秩、一秩映射,则分别称a是中的紧元、有限维元、一维元;如果对任意x,y∈,xay=0蕴涵xa=0或ay=0,则称a为中的single元,如果C-代数中的任两个非零理想的积仍是非零的,则称是素的,近年来对于C-代数上乘子及初等算子有不少文献作了深入探讨,
基金the National Natural Science Foundation of China,and the Natural Science Foundation of Shanxi Province and the Youth Scientific
文摘This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X. First, the sufficient and necessary conditions for a local C-semigroup and a C-cosine function to be the restriction of a global C-semigroup and a global C-cosine function to an interval are given, respectively. Secondly, it is characterized for a closed operator to be the generator of a local C-semigroup and a local C-cosine function, respectively.
文摘in this paper, we first give a Hille-Yosida type sufficient and necessary conditionfor n-times integrated mild C-existence families. Then, we present a Laplace type sufficientand necessary condition for exponentially bounded n-times integrated C-semigrougs, andstudy the relationship between integrated regularized semigroups and general regularizedsemigroups. Finally, we offer a characterization of integrated C-semigroups in terms of thesolvability of abstract Cauchy problems.
文摘By defined holomorphic n-times integrated mild C-existence families and Csemigroups, their relationship with holomorphic mild C1-exustence families and holomorphic C1 -semigroups is discussed, respectively. For exponentially bounded cases, this papergives several Hille-Yosida type conditions for an operator to have (or generate) one of thesefamilies of operators and generalize the corresponding results in [1], [2] and [3]. These families by the holomorphic solvability of the abstract Cauchy problem is also characterized.
基金Project supported by the National Natural Science Foundation of China.
文摘Let X be a separable complex Hilbert space, B(X)the set of all (bounded linear)operators acting on X. For T∈B(X), the question whether T can be factorized into the product of some good operators has been discussed by many authors (e. g. Ref. [1]—[6]). In [1], Wu obtained some sufficient and necessary conditions for an operator to be a prod-
