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B-Fredholm and Drazin invertible operators through localized SVEP

M. AmouchH. Zguitti — 2011

Mathematica Bohemica

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 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.

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

M. AmouchH. Zguitti — 2008

Mathematica Bohemica

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.

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