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On Quasi-Normality of Two-Sided Multiplication

Amouch, M. — 2009

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 47B47, 47B10, 47A30. In this note, we characterize quasi-normality of two-sided multiplication, restricted to a norm ideal and we extend this result, to an important class which contains all quasi-normal operators. Also we give some applications of this result.

B-Fredholm and Drazin invertible operators through localized SVEP

M. Amouch; H. 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 $λ \in ℂ$ 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.

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

M. Amouch; H. 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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On Quasi-Normality of Two-Sided Multiplication

B-Fredholm and Drazin invertible operators through localized SVEP

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

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