Two classes of operators with irreducibility and the small and compact perturbations of them
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| 024 | 7 | 0 | |a 10.1007/s10114-015-4661-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-4661-2 | ||
| 245 | 0 | 0 | |a Two classes of operators with irreducibility and the small and compact perturbations of them |h [Elektronische Daten] |c [Yun Zhang, Li Lin] |
| 520 | 3 | |a 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}. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Banach spaces |2 nationallicence | |
| 690 | 7 | |a strongly irreducible operators |2 nationallicence | |
| 690 | 7 | |a operators with irreducibility |2 nationallicence | |
| 690 | 7 | |a small and compact perturbations |2 nationallicence | |
| 700 | 1 | |a Zhang |D Yun |u School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, P. R. China |4 aut | |
| 700 | 1 | |a Lin |D Li |u College of Mathematics and Computer Science, Fuzhou University, 350002, Fuzhou, P. R. China |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/8(2015-08-01), 1261-1272 |x 1439-8516 |q 31:8<1261 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-4661-2 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-4661-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zhang |D Yun |u School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Lin |D Li |u College of Mathematics and Computer Science, Fuzhou University, 350002, Fuzhou, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/8(2015-08-01), 1261-1272 |x 1439-8516 |q 31:8<1261 |1 2015 |2 31 |o 10114 | ||