Gelfand-Mazur theorems in normed algebras: a survey
type: Item
instance of: scholarly article
title: Gelfand-Mazur theorems in normed algebras: a survey
zbMATH Open document ID: 1398.46038
author: S. H. Kulkarni
author: S. J. Bhatt
published in: Expositiones Mathematicae
publication date: 2018-06-13T00:00:00Z
review text: The paper is a survey of results generalizing the well-known Gelfand-Mazur theorem, mainly for the class of Banach algebras. No proofs are presented. The discussion gives some good hints about most of the proofs and all results are clearly supplied with the references, where the interested reader can find the proofs. Although in the Section~8(e), some words are said about more general (non-normed, not locally convex) topological algebras, references to the works of \textit{M. Abel} [Uch. Zap. Tartu. Gos. Univ. 899, 65--70 (1990; Zbl 0762.46038); Contemp. Math. 341, 17--24 (2004; Zbl 1054.46027)], of \textit{M. Abel'} and \textit{A. Kokk} [Izv. Akad. Nauk Èst. SSR, Fiz., Mat. 37, No. 4, 377--386 (1988; Zbl 0677.46030)], or to the work [Topol. Algebra Appl. 2, 19--23 (2014; Zbl 1316.46040)] of \textit{E. Anjidani} could have been provided.
reviewed by: Mart Abel
Mathematics Subject Classification ID: 46H20
Mathematics Subject Classification ID: 46-02
zbMATH DE Number: 6887413
zbMATH Keywords: Banach algebra
zbMATH Keywords: division algebra
zbMATH Keywords: Gelfand-Mazur theorem
zbMATH Keywords: spectral algebra
zbMATH Keywords: normed algebra
MaRDI profile type: Publication
full work available at URL: j.exmath.2017.08.004
OpenAlex ID: W2751070615
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DOI: 10.1016/J.EXMATH.2017.08.004
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