The spectrum of an element in a Banach-Kantorovich algebra over a ring of measurable functions
type: Item
instance of: scholarly article
title: The spectrum of an element in a Banach-Kantorovich algebra over a ring of measurable functions
zbMATH Open document ID: 1485.46052
author: Allabay Arziev
author: K. Kudaybergenov
published in: Advances in Operator Theory
publication date: 2021-12-27T00:00:00Z
review text: Each Banach-Kantorovich algebra over a ring of measurable functions is shown to be representable as a measurable bundle of Banach algebras with a vector-valued lifting. This enables the authors to prove that the spectrum of each element of such an algebra is nonempty and cyclically compact. The genuine value of the results may be better understood by using Boolean valued analysis, and the authors refer to \textit{A. E. Gutman} [Sib. Adv. Math. 3, No. 4, 8--40 (1993; Zbl 0854.46005)].
Mathematics Subject Classification ID: 46H25
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46M20
zbMATH DE Number: 7450835
zbMATH Keywords: Banach-Kantorovich algebra
zbMATH Keywords: measurable function
zbMATH Keywords: cyclical compactness
zbMATH Keywords: spectrum
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
full work available at URL: s43036-021-00176-9
OpenAlex ID: W4200295696
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DOI: 10.1007/S43036-021-00176-9
description: scientific article; zbMATH DE number 7450835