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http://dx.doi.org/10.4134/BKMS.2012.49.5.1027

WEYL TYPE-THEOREMS FOR DIRECT SUMS  

Berkani, Mohammed (Department of mathematics Science Faculty of Oujda University Mohammed I Operator theory team, SFO)
Zariouh, Hassan (Department of mathematics Science Faculty of Meknes University Moulay Ismail)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 1027-1040 More about this Journal
Abstract
The aim of this paper is to study the Weyl type-theorems for the orthogonal direct sum $S{\oplus}T$, where S and T are bounded linear operators acting on a Banach space X. Among other results, we prove that if both T and S possesses property ($gb$) and if ${\Pi}(T){\subset}{\sigma}_a(S)$, ${\PI}(S){\subset}{\sigma}_a(T)$, then $S{\oplus}T$ possesses property ($gb$) if and only if ${\sigma}_{SBF^-_+}(S{\oplus}T)={\sigma}_{SBF^-_+}(S){\cup}{\sigma}_{SBF^-_+}(T)$. Moreover, we prove that if T and S both satisfies generalized Browder's theorem, then $S{\oplus}T$ satis es generalized Browder's theorem if and only if ${\sigma}_{BW}(S{\oplus}T)={\sigma}_{BW}(S){\cup}{\sigma}_{BW}(T)$.
Keywords
property (gb); property (b); property (gw); direct sums; essential semi-B-Fredholm spectrum;
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