Property (gz) for bounded linear operators

Authors

  • H. Zariouh Department of Mathematics, Science Faculty of Meknes, University Moulay Ismail, BP 11201, Zitoune, Meknes, Morocco Author

Keywords:

Property (z), property (gz), property (az), essential semi-B-Fredholm spectrum

Subjects:

47A53, 47A10, 47A11

Abstract

A bounded linear operator T acting on a Banachspace possesses property (gaw) if σ(T)\setminusEa(T)=σBW(T), where σBW(T) is the B-Weylspectrum of T, σ(T) is the usual spectrum of T andEa(T) is the set of all eigenvalues of T which are isolatedin the approximate point spectrum of T. In this paper weintroduce and study the new spectral properties (z), (gz), (az)and (gaz) as a continuation of [M. Berkani, H. Zariouh, {ıt New extended Weyl type theorems},Mat. Vesnik {\bf 62} (2010), 145–154], which are related toWeyl type theorems. Among other results, we prove that Tpossesses property (gz) if and only if T possesses property(gaw) and σBW(T)=σSBF+(T); whereσSBF+(T) is the essential semi-B-Fredholm spectrum of T.

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Published

2013-01-15