caa a22 4500 60546197X CHVBK 20210128100246.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10114-015-4661-2 doi (NATIONALLICENCE)springer-10.1007/s10114-015-4661-2 Two classes of operators with irreducibility and the small and compact perturbations of them [Elektronische Daten] [Yun Zhang, Li Lin] 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 (ΣFDI)(X) with respect to the strong-operator topology and every compact operator K can be approximated by operators in (ΣFDI)(X) with respect to the norm topology on a Banach space X with a Schauder basis, where (ΣFDI)(X):= {T ∈ B(X): T = Σ i=1 k ⊕T i , T i ∈ (FDI), k ∈ ℕ}. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Banach spaces nationallicence strongly irreducible operators nationallicence operators with irreducibility nationallicence small and compact perturbations nationallicence Zhang Yun School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, P. R. China aut Lin Li College of Mathematics and Computer Science, Fuzhou University, 350002, Fuzhou, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/8(2015-08-01), 1261-1272 1439-8516 31:8<1261 2015 31 10114 https://doi.org/10.1007/s10114-015-4661-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4661-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhang Yun School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, P. R. China aut NATIONALLICENCE 700 1- Lin Li College of Mathematics and Computer Science, Fuzhou University, 350002, Fuzhou, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/8(2015-08-01), 1261-1272 1439-8516 31:8<1261 2015 31 10114