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arXiv · 1805.08741

Pseudo-B-Fredholm operators, poles of the resolvent and mean convergence in the Calkin Algebra

Mohammed Berkani·Snežana Č. Živković-Zlatanović
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Abstract

We define here a pseudo B-Fredholm operator as an operator such that 0 is isolated in its essential spectrum, then we prove that an operator $T$ is pseudo- B-Fredholm if and only if $T = R + F$ where $R$ is a Riesz operator and $F$ is a B-Fredholm operator such that the commutator $[R,\, F]$ is compact. Moreover, we prove that 0 is a pole of the resolvent of an operator $T$ in the Calkin algebra if and only if $T= K+F$, where $K$ is a power compact operator and $F$ is a B-Fredholm operator, such that the commutator $[K,\, F]$ is compact. As an application, we characterize the mean convergence in the Calkin algebra.

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Mohammed Berkani, Snežana Č. Živković-Zlatanović. 2018-05-22. Pseudo-B-Fredholm operators, poles of the resolvent and mean convergence in the Calkin Algebra. https://arxiv.org/abs/1805.08741

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