Authors
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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 acting on a Banachspace possesses property (gaw) if , where is the B-Weylspectrum of , is the usual spectrum of and is the set of all eigenvalues of which are isolatedin the approximate point spectrum of . 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 possesses property (gz) if and only if possesses property(gaw) and ; where is the essential semi-B-Fredholm spectrum of .