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

2020/10/13 by Berkani, Mohammed
#FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2010.07040

Abstract

In this paper, we define an analytical index for continuous families of Fredholm operators parameterized by a topological space \mathbbX into a Banach space X. We also consider the Weyl spectrum for continuous families of bounded linear operators and we study its continuity.

Related

• A new approach in index theory
• Index of continuous semi-Fredholm families, regularities and semiregularities
• A handy formula for the Fredholm index of Toeplitz plus Hankel operators
• Spectrum of a family of operators
• Local spectrum of a family of operators