设 X,Y是BanaCh 空间,B（X,Y）表示 X 到 Y 的有界线性算子全体,Ai∈B（X,Y）（i=1,2,…,n）.本文给出了 A1,A2,…,An线性相关的几个充要条件,及其应用,并给出一个反例,指出[1]中的引理2是错误的.定理1 设 A,B∈B（X,Y）,则下列命题等价...设 X,Y是BanaCh 空间,B（X,Y）表示 X 到 Y 的有界线性算子全体,Ai∈B（X,Y）（i=1,2,…,n）.本文给出了 A1,A2,…,An线性相关的几个充要条件,及其应用,并给出一个反例,指出[1]中的引理2是错误的.定理1 设 A,B∈B（X,Y）,则下列命题等价.（1）A,B 线性相关.展开更多
B. Sz-Nagy and C. Foias introduced the concept of quasisimilarity in 1967. Since then, the quasisimilarity of operators has become an important research problem in the theory of operators and a lot of attractive resul...B. Sz-Nagy and C. Foias introduced the concept of quasisimilarity in 1967. Since then, the quasisimilarity of operators has become an important research problem in the theory of operators and a lot of attractive results have been obtained. But, as regards intersection relations between some subsets of the spectrum σ(A)and those of the spectrum σ(B), where A and B are quasisimilar operators, comparatively few results have been delivered.展开更多
Lambert showed in 1970 that two quasisimilar injective unilateral weighted shifts must be similar and hence have the same dosed range points. But whether the conclusion is true for injective bilateral weighted shift o...Lambert showed in 1970 that two quasisimilar injective unilateral weighted shifts must be similar and hence have the same dosed range points. But whether the conclusion is true for injective bilateral weighted shift operators has not been proved yet. In this note we answer the question affirmatively with a stronger result. We prove that two quasisimilar injective bilat-展开更多
Let A and B be quasisimilar operators. We describe refinedly the intersection relationsof the components of various essential spectra of A with various subsets of the essentialspectrum of B, and give an affirmative an...Let A and B be quasisimilar operators. We describe refinedly the intersection relationsof the components of various essential spectra of A with various subsets of the essentialspectrum of B, and give an affirmative answer to a question posed by L. A. Fialkow.展开更多
文摘B. Sz-Nagy and C. Foias introduced the concept of quasisimilarity in 1967. Since then, the quasisimilarity of operators has become an important research problem in the theory of operators and a lot of attractive results have been obtained. But, as regards intersection relations between some subsets of the spectrum σ(A)and those of the spectrum σ(B), where A and B are quasisimilar operators, comparatively few results have been delivered.
文摘Lambert showed in 1970 that two quasisimilar injective unilateral weighted shifts must be similar and hence have the same dosed range points. But whether the conclusion is true for injective bilateral weighted shift operators has not been proved yet. In this note we answer the question affirmatively with a stronger result. We prove that two quasisimilar injective bilat-
基金Project supported by a grant from the Fujian Province Natural Science Foundation.
文摘Let A and B be quasisimilar operators. We describe refinedly the intersection relationsof the components of various essential spectra of A with various subsets of the essentialspectrum of B, and give an affirmative answer to a question posed by L. A. Fialkow.
