The index of operators in Banach spaces
type: Item
instance of: scholarly article
title: The index of operators in Banach spaces
zbMATH Open document ID: 0654.47001
DOI: 10.1007/BF01201704
published in: Integral Equations and Operator Theory
publication date: 1985-01-01T00:00:00Z
review text: The notion of index of an operator is a central one in the theory which leads to the famous Atiyah-Singer theorem, one of the highlights of modern Global Analysis. In this paper I want to give an historical sketch of the development of that notion during the first half of the 20th century, providing the tools of ``Functional Analysis'' used in the Atiyah-Singer proof.
Mathematics Subject Classification ID: 47-03
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 58J20
zbMATH DE Number: 4067650
zbMATH Keywords: index of an operator
zbMATH Keywords: Atiyah-Singer theorem
author: Jean A. Dieudonné
MaRDI profile type: Publication
cites work: Q5784673
cites work: Perturbation theory for nullity, deficiency and other quantities of linear operators
cites work: Störungstheorie der Spektralzerlegung. I. Analytische Störung der isolierten Punkteigenwerte eines beschränkten Operators
cites work: Operators with a Fredholm Theory
cites work: Q5818766
cites work: Properties of linear transformations preserved under addition of a completely continuous transformation
full work available at URL: https://doi.org/10.1007/bf01201704
OpenAlex ID: W2169264193
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description: scientific article; zbMATH DE number 4067650