Extended Weyl-Type Theorems for Direct Sums
| Autor: | Berkani M., Kachad M., Zariouh H. |
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| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Demonstratio Mathematica, Vol 47, Iss 2, Pp 411-422 (2014) |
| Druh dokumentu: | article |
| ISSN: | 0420-1213 2391-4661 |
| DOI: | 10.2478/dema-2014-0032 |
| Popis: | In this paper, we study the stability of extended Weyl and Browdertype theorems for orthogonal direct sum S⊕T, where S and T are bounded linear operators acting on Banach space. Two counterexamples shows that property (ab), in general, is not preserved under direct sum. Nonetheless, and under the assumptions that Π0α (T) ⊂σα(S) and Π0α(S) ⊂σα(T), we characterize preservation of property (ab) under direct sum S⊕T. Furthermore, we show that if S and T satisfy generalized a-Browder’s theorem, then S⊕T satisfies generalized a-Browder’s theorem if and only if σSBF-+ (S ⊕T) = σSBF-+(S) ∪σSBF-+(T), which improves a recent result of [13] by removing certain extra assumptions. |
| Databáze: | Directory of Open Access Journals |
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