Index of continuous families of bounded linear operators in Banach spaces and application
Mohammed Berkani

TL;DR
This paper introduces an analytical index for continuous families of Fredholm operators in Banach spaces, explores the Weyl spectrum's properties, and investigates its continuity, contributing to operator theory and spectral analysis.
Contribution
It defines a new analytical index for parameterized Fredholm operators and studies the continuity of the Weyl spectrum in Banach spaces.
Findings
Defined an analytical index for continuous families of Fredholm operators
Analyzed the Weyl spectrum's continuity properties
Extended spectral theory in the context of Banach spaces
Abstract
In this paper, we define an analytical index for continuous families of Fredholm operators parameterized by a topological space into a Banach space We also consider the Weyl spectrum for continuous families of bounded linear operators and we study its continuity.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Holomorphic and Operator Theory · Matrix Theory and Algorithms
