A trace formula for the index of B-Fredholm operators

Mohammed Berkani

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arXiv · 1609.01695

A trace formula for the index of B-Fredholm operators

Mohammed Berkani

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Abstract

In this paper we define B-Fredholm elements in a Banach algebra $A$ modulo an ideal $J$ of $A.$ When a trace function is given on the ideal $J,$ it generate an index for B-Fredholm elements. In the case of a B-Fredholm operator $T$ acting on a Banach space, we prove that its usual index $ind(T)$ is equal to the trace of the commutator $ [T, T_0],$ where $T_0$ is a Drazin inverse of $T$ modulo the ideal of finite rank operators, extending a Fedosov's trace formula for Fredholm operators. In the case of a semi-simple Banach algebra, we prove a punctured neighborhood theorem for the index.

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BibTeX RIS

Mohammed Berkani. 2016-09-06. A trace formula for the index of B-Fredholm operators. https://arxiv.org/abs/1609.01695

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