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Extended Weyl-type theorems for direct sums

Berkani M., Kachad M., Zariouh H.

Demonstratio Mathematica

2014

Vol. 47, nr 2

411--422

In this paper, we study the stability of extended Weyl and Browdertype theorems for orthogonal direct sum (...), 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 (…), we characterize preservation of property (ab) under direct sum (...). Furthermore, we show that if S and T satisfy generalized a-Browder’s theorem, then (...) satisfies generalized a-Browder’s theorem if and only if (…), which improves a recent result of [13] by removing certain extra assumptions.