| Autor: |
Berkani, M., Kachad, M., Zariouh, H. |
| Předmět: |
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| Zdroj: |
Demonstratio Mathematica; Mar2018, Vol. 51 Issue 1, p411-422, 12p |
| Abstrakt: |
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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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