The Weyl's theorem and its perturbations in semisimple Banach algebra
type: Item
instance of: scholarly article
title: The Weyl's theorem and its perturbations in semisimple Banach algebra
zbMATH Open document ID: 1481.46042
author: Ying Ying Kong
author: Lining Jiang
author: Yan Xun Ren
publication date: 2021-07-28T00:00:00Z
review text: The classical theories of Fredholm and Riesz operators on infinite-dimensional Banach spaces were extented to general Banach algebras by B. A. Barnes, L. D. Pearlman, M. R. F. Smyth, R. E. Harte, C. Schmoeger and many others. The book of B. A. Barnes, G. J. Murphy, M. R. F. Smyth, and T. T. West [\textit{B. A. Barnes} et al., Riesz and Fredholm theory in Banach algebras. Boston-London-Melbourne: Pitman Advanced Publishing Program (1982; Zbl 0534.46034)] gives a nice overwiev of those extended theories. In the paper under review the authors define Fredholm, Weyl and Browder elements in a unital semisimple Banach algebra \(\mathcal{A}\) and prove some properties of them. They give equivalent conditions in order that Weyl's and Browder's theorems hold for an element \(a\in\mathcal{A}\) and for some of its perturbations, or images by holomorphic functions.
Mathematics Subject Classification ID: 46H99
Mathematics Subject Classification ID: 47B01
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 7375664
zbMATH Keywords: perturbation
zbMATH Keywords: Weyl's theorem
zbMATH Keywords: semisimple Banach algebra
zbMATH Keywords: Fredholm element
zbMATH Keywords: Browder element
reviewed by: Andrzej Sołtysiak
MaRDI profile type: Publication
full work available at URL: s10114-021-0434-2
OpenAlex ID: W3162884534
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DOI: 10.1007/S10114-021-0434-2
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 7375664