Displaying similar documents to “B-Fredholm and Drazin invertible operators through localized SVEP”

A note on the a -Browder’s and a -Weyl’s theorems

M. Amouch, H. Zguitti (2008)

Mathematica Bohemica

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Let T be a Banach space operator. In this paper we characterize a -Browder’s theorem for T by the localized single valued extension property. Also, we characterize a -Weyl’s theorem under the condition E a ( T ) = π a ( T ) , where E a ( T ) is the set of all eigenvalues of T which are isolated in the approximate point spectrum and π a ( T ) is the set of all left poles of T . Some applications are also given.

Extended Weyl type theorems

M. Berkani, H. Zariouh (2009)

Mathematica Bohemica

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An operator T acting on a Banach space X possesses property ( gw ) if σ a ( T ) ∖ σ SBF + - ( T ) = E ( T ) , where σ a ( T ) is the approximate point spectrum of T , σ SBF + - ( T ) is the essential semi-B-Fredholm spectrum of T and E ( T ) is the set of all isolated eigenvalues of T . In this paper we introduce and study two new properties ( b ) and ( gb ) in connection with Weyl type theorems, which are analogous respectively to Browder’s theorem and generalized Browder’s theorem. Among other, we prove that if T is a bounded linear operator acting on a Banach space...

Spectra originating from semi-B-Fredholm theory and commuting perturbations

Qingping Zeng, Qiaofen Jiang, Huaijie Zhong (2013)

Studia Mathematica

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Burgos, Kaidi, Mbekhta and Oudghiri [J. Operator Theory 56 (2006)] provided an affirmative answer to a question of Kaashoek and Lay and proved that an operator F is of power finite rank if and only if σ d s c ( T + F ) = σ d s c ( T ) for every operator T commuting with F. Later, several authors extended this result to the essential descent spectrum, left Drazin spectrum and left essential Drazin spectrum. In this paper, using the theory of operators with eventual topological uniform descent and the technique used...

Restriction of an operator to the range of its powers

M. Berkani (2000)

Studia Mathematica

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Let T be a bounded linear operator acting on a Banach space X. For each integer n, define T n to be the restriction of T to R ( T n ) viewed as a map from R ( T n ) into R ( T n ) . In [1] and [2] we have characterized operators T such that for a given integer n, the operator T n is a Fredholm or a semi-Fredholm operator. We continue those investigations and we study the cases where T n belongs to a given regularity in the sense defined by Kordula and Müller in[10]. We also consider the regularity of operators with...

The index for Fredholm elements in a Banach algebra via a trace II

Jacobus J. Grobler, Heinrich Raubenheimer, Andre Swartz (2016)

Czechoslovak Mathematical Journal

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We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index.

A note on the index of B -Fredholm operators

M. Berkani, Dagmar Medková (2004)

Mathematica Bohemica

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From Corollary 3.5 in [Berkani, M; Sarih, M.; Studia Math. 148 (2001), 251–257] we know that if S , T are commuting B -Fredholm operators acting on a Banach space X , then S T is a B -Fredholm operator. In this note we show that in general we do not have error ( S T ) = error ( S ) + error ( T ) , contrarily to what has been announced in Theorem 3.2 in [Berkani, M; Proc. Amer. Math. Soc. 130 (2002), 1717–1723]. However, if there exist U , V ∈ L ( X ) such that S , T , U , V are commuting and U S + V T = I , then error ( S T ) = error ( S ) + error ( T ) , where error stands for the index of a B -Fredholm...