This paper shows that every operator which is quasisimilar to strongly irreducible Cowen-Douglas operators is still strongly irreducible. This result answers a question posted by Davidson and Herrero (ref. [1]).
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
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 X denote an infinite dimensional complex Banach space and L(X) denote the set of all the bounded linear operators on X. For A∈L(X), B∈L (Y), A and B are quasisimilar (written as A (?) B) if there exist P:X→Y, Q...Let X denote an infinite dimensional complex Banach space and L(X) denote the set of all the bounded linear operators on X. For A∈L(X), B∈L (Y), A and B are quasisimilar (written as A (?) B) if there exist P:X→Y, Q: Y→X, where P and Q are bounded linear, injective and dense-ranged such that PA=BP, QB=AQ. T. B.展开更多
Yang Liming showed in 1988 that if S is a subnormal operator, T is a hyponormal operator and T and S are quasisimilar, then σ_e(S)(?) σ_e(T), and hence he deduced the conclusion that two quasisimilar subnormal opera...Yang Liming showed in 1988 that if S is a subnormal operator, T is a hyponormal operator and T and S are quasisimilar, then σ_e(S)(?) σ_e(T), and hence he deduced the conclusion that two quasisimilar subnormal operators have equal essential spectra. This is an important result in the theory of quasisimilarity. In this note we improve Yang’s method to show that if S or S is subnormal, T is a bounded linear operator and T and S are quasisimilar, then σ_e(S) (?) σ_e(T).展开更多
An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(...An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.展开更多
基金This work was supported by the 973 Project of China and the National Natural Science Foundation of China (Grant No. 19631070).
文摘This paper shows that every operator which is quasisimilar to strongly irreducible Cowen-Douglas operators is still strongly irreducible. This result answers a question posted by Davidson and Herrero (ref. [1]).
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.
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 the Science Foundation of Fujian Province.
文摘Let X denote an infinite dimensional complex Banach space and L(X) denote the set of all the bounded linear operators on X. For A∈L(X), B∈L (Y), A and B are quasisimilar (written as A (?) B) if there exist P:X→Y, Q: Y→X, where P and Q are bounded linear, injective and dense-ranged such that PA=BP, QB=AQ. T. B.
基金Project supported by the Science Foundation of Fujian Province
文摘Yang Liming showed in 1988 that if S is a subnormal operator, T is a hyponormal operator and T and S are quasisimilar, then σ_e(S)(?) σ_e(T), and hence he deduced the conclusion that two quasisimilar subnormal operators have equal essential spectra. This is an important result in the theory of quasisimilarity. In this note we improve Yang’s method to show that if S or S is subnormal, T is a bounded linear operator and T and S are quasisimilar, then σ_e(S) (?) σ_e(T).
基金Supported by the Natural Science Foundation of the Department of Education of Henan Province（12B110025, 102300410012）
文摘An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.
