This paper gives the concepts of finite dimensional irreducible operators（（FDI） operators）and infinite dimensional irreducible operators（（IDI） operators）. Discusses the relationships of（FDI）operators,（IDI）...This paper gives the concepts of finite dimensional irreducible operators（（FDI） operators）and infinite dimensional irreducible operators（（IDI） operators）. Discusses the relationships of（FDI）operators,（IDI） operators and strongly irreducible operators（（SI） operators） and illustrates some properties of the three classes of operators. Some sufficient conditions for the finite-dimensional irreducibility of operators which have the forms of upper triangular operator matrices are given. This paper proves that every operator with a singleton spectrum is a small compact perturbation of an（FDI） operator on separable Banach spaces and shows that every bounded linear operator T can be approximated by operators in（Σ FDI）（X） with respect to the strong-operator topology and every compact operator K can be approximated by operators in（Σ FDI）（X） with respect to the norm topology on a Banach space X with a Schauder basis, where（ΣFDI）（X） ：= {T∈B（X） ： T=Σki=1Ti, Ti ∈（FDI）, k ∈ N}.展开更多
Let Mc = （ A0CB ） be a 2 × 2 upper triangular operator matrix acting on the Banach space X × Y. We prove that σr（A） ∪ σr（ B）= σr （Mc） ∪ W ,where W is the union of certain of the holes in σr（Mc...Let Mc = （ A0CB ） be a 2 × 2 upper triangular operator matrix acting on the Banach space X × Y. We prove that σr（A） ∪ σr（ B）= σr （Mc） ∪ W ,where W is the union of certain of the holes in σr（Mc） which happen to be subsets of σr（A） ∩ σr（B）, and σr（A）, σr（B）, σr（Mc） can be equal to the Browder or essential spectra of A, B, Mc, respectively. We also show that the above result isn＇t true for the Kato spectrum, left （right） essential spectrum and left （right） spectrum.展开更多
We obtain the K-groups of the operator ideals contained in the class of Riesz operators. And based on the results, we calculate the K-groups of the operator algebras on HD nspaces and QDn spaces.
基金Supported by National Natural Science Foundation of China(Grant Nos.11401101,11201071 and 11171066)Fujian Natural Science Foundation(Grant No.2013J05004)Foundation of Fuzhou University(Grant Nos.2013-XQ-33 and XRC-1259)
文摘This paper gives the concepts of finite dimensional irreducible operators（（FDI） operators）and infinite dimensional irreducible operators（（IDI） operators）. Discusses the relationships of（FDI）operators,（IDI） operators and strongly irreducible operators（（SI） operators） and illustrates some properties of the three classes of operators. Some sufficient conditions for the finite-dimensional irreducibility of operators which have the forms of upper triangular operator matrices are given. This paper proves that every operator with a singleton spectrum is a small compact perturbation of an（FDI） operator on separable Banach spaces and shows that every bounded linear operator T can be approximated by operators in（Σ FDI）（X） with respect to the strong-operator topology and every compact operator K can be approximated by operators in（Σ FDI）（X） with respect to the norm topology on a Banach space X with a Schauder basis, where（ΣFDI）（X） ：= {T∈B（X） ： T=Σki=1Ti, Ti ∈（FDI）, k ∈ N}.
基金the National Natural Science Foundation of China (Grants NO.10471025,NO.10771034)the Natural Science Foundation of Fujian Province of China(Grant NO.S0650009)+1 种基金the Education Department Foundation of Fujian Province of China (Grants NO.JA05211,NO.JB06026)the Foundation of Technology and Development of Fuzhou University(Grant NO.2007-XY-11)
文摘Let Mc = （ A0CB ） be a 2 × 2 upper triangular operator matrix acting on the Banach space X × Y. We prove that σr（A） ∪ σr（ B）= σr （Mc） ∪ W ,where W is the union of certain of the holes in σr（Mc） which happen to be subsets of σr（A） ∩ σr（B）, and σr（A）, σr（B）, σr（Mc） can be equal to the Browder or essential spectra of A, B, Mc, respectively. We also show that the above result isn＇t true for the Kato spectrum, left （right） essential spectrum and left （right） spectrum.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10926173 and 10771034)Natural Science Foundation of Fujian Province of China (Grant No. 2009J05002)Foundation of Technology and Development of Fuzhou University (Grant No. 2007-XY-11)
文摘We obtain the K-groups of the operator ideals contained in the class of Riesz operators. And based on the results, we calculate the K-groups of the operator algebras on HD nspaces and QDn spaces.
