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...

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

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

A note on the index of $B$ -Fredholm operators