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arXiv · 2401.01390

Fredholm-type Operators and Index

Alaa Hamdan·Mohammed Berkani
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Abstract

While in \cite{HB} we studied classes of Fredholm-type operators defined by the homomorphism $\Pi$ from $L(X)$ onto the Calkin algebra $\mathcal{C}(X)$, $X$ being a Banach space, we study in this paper two classes of Fredholm-type operators defined by the homomorphism $\pi$ from $L(X)$ onto the algebra $\mathcal{C}_0(X)= L(X)/F_0(X),$ where $F_0(X)$ is the ideal of finite rank operators in $L(X).$ Then we define an index for Fredholm-type operators and we show that this new index satisfies similar properties as the usual Fredholm index.

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Alaa Hamdan, Mohammed Berkani. 2024-01-02. Fredholm-type Operators and Index. https://arxiv.org/abs/2401.01390

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