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]).
This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly irreducible operators on Banach spaces with w＊-separable dual. It also gives some prop...This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly irreducible operators on Banach spaces with w＊-separable dual. It also gives some properties of strongly irreducible operators on Banach spaces. In particular, if T is a strongly irreducible operator on an infinite-dimensional Banach space, then T is not of finite rank and T is not an algebraic operator. On Banach spaces with subsymmetric bases, including infinite-dimensional separable Hilbert spaces, it shows that quasisimilarity does not preserve strong irreducibility. In addition, we show that the strong irreducibility of an operator does not imply the strong irreducibility of its conjugate operator, which is not the same as the property in Hilbert spaces.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Supported by National Natural Science Foundation of China(Grant Nos.10926173,11171066 and 10771034)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.2010350311001)Natural Science Foundation of Fujian Province of China(Grant No.2009J05002)
文摘This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly irreducible operators on Banach spaces with w＊-separable dual. It also gives some properties of strongly irreducible operators on Banach spaces. In particular, if T is a strongly irreducible operator on an infinite-dimensional Banach space, then T is not of finite rank and T is not an algebraic operator. On Banach spaces with subsymmetric bases, including infinite-dimensional separable Hilbert spaces, it shows that quasisimilarity does not preserve strong irreducibility. In addition, we show that the strong irreducibility of an operator does not imply the strong irreducibility of its conjugate operator, which is not the same as the property in Hilbert spaces.
