Extended Weyl type theorems

M. Berkani; H. Zariouh

Displaying similar documents to “Extended Weyl type theorems”

Ascent, descent and roots of Fredholm operators

Bertram Yood (2003)

Studia Mathematica

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Let T be a Fredholm operator on a Banach space. Say T is rootless if there is no bounded linear operator S and no positive integer m ≥ 2 such that $S^{m} = T$ . Criteria and examples of rootlessness are given. This leads to a study of ascent and descent whether finite or infinite for T with examples having infinite ascent and descent.

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.

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 $U, V \in L (X)$ 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...

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 $λ \in ℂ$ 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.

Displaying similar documents to “Extended Weyl type theorems”

Ascent, descent and roots of Fredholm operators

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

A note on the index of B -Fredholm operators

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 index of $B$ -Fredholm operators