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Displaying similar documents to “A note on the a -Browder’s and a -Weyl’s theorems”

Single valued extension property and generalized Weyl’s theorem

M. Berkani, N. Castro, S. V. Djordjević (2006)

Mathematica Bohemica

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Let T be an operator acting on a Banach space X , let σ ( T ) and σ B W ( T ) be respectively the spectrum and the B-Weyl spectrum of T . We say that T satisfies the generalized Weyl’s theorem if σ B W ( T ) = σ ( T ) ∖ E ( T ) , where E ( T ) is the set of all isolated eigenvalues of T . The first goal of this paper is to show that if T is an operator of topological uniform descent and 0 is an accumulation point of the point spectrum of T , then T does not have the single valued extension property at 0 , extending an earlier result of J. K. Finch...

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...

B-Fredholm and Drazin invertible operators through localized SVEP

M. Amouch, H. Zguitti (2011)

Mathematica Bohemica

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Let X be a Banach space and T be a bounded linear operator on X . We denote by S ( T ) the set of all complex λ ∈ ℂ such that T does not have the single-valued extension property at λ . In this note we prove equality up to S ( T ) between the left Drazin spectrum, the upper semi-B-Fredholm spectrum and the semi-essential approximate point spectrum. As applications, we investigate generalized Weyl’s theorem for operator matrices and multiplier operators.