Extended Weyl-Type Theorems for Direct Sums

Demonstratio mathematica

article

M. Berkani¹  M. Kachad¹  H. Zariouh² 

[1] DEPARTMENT OF MATHEMATICS SCIENCE FACULTY OF OUJDA UNIVERSITY MOHAMMED I OPERATOR THEORY TEAM;CENTRE RÉGIONAL DES MÉTIERS DE L’ÉDUCARION ET DE FORMATION;EQUIPE DE LA THÉORIE DES OPÉRATEURS UNIVERSITÉ MOHAMMED I FACULTÉ DES SCIENCES D’OUJDA DÉPT. DE MATHEMATIQUES MAROCCO

关键词: property pgabq;    property pgawq;    direct sums;    B-Weyl spectrum;   

DOI  :  10.2478/dema-2014-0032

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

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 Π 0 α (T) ⊂σ α (S) and Π 0 α (S) ⊂σ α (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 σ SBF - + (S ⊕T) = σ SBF - + (S) ∪ σSBF - + (T), which improves a recent result of [13] by removing certain extra assumptions.

【 授权许可】

CC BY