Berkani, M. and Sarih, M. and Zariouh, H. (2016) A-Browder-type theorems for direct sums of operators. Mathematica Bohemica, 141 (1). pp. 99-108.

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We study the stability of a-Browder-type theorems for orthogonal direct sums of operators. We give counterexamples which show that in general the properties (SBaw), (SBab), (SBw) and (SBb) are not preserved under direct sums of operators. However, we prove that if S and T are bounded linear operators acting on Banach spaces and having the property (SBab), then S ⊕ T has the property (SBab) if and only if (Formula Presented) where (Formula Presented) is the upper semi-B-Weyl spectrum of T. We obtain analogous preservation results for the properties (SBaw), (SBb) and (SBw) with extra assumptions. © 2016, Akademie ved Ceske Republiky. All rights reserved.

Item Type: Article
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48

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