Gelfand theory of reduced group \(L^p\)-operator algebra
type: Item
instance of: scholarly article
title: Gelfand theory of reduced group \(L^p\)-operator algebra
zbMATH Open document ID: 1493.22003
author: Zhen Wang
author: Yuedi Zeng
published in: Annals of Functional Analysis
publication date: 2021-12-24T00:00:00Z
review text: Let \(G\) be a locally compact abelian group and \(\lambda_p\) the left regular representation of \(G\) on \(L^p(G)\) (\(p\geq 1\)). The representation induces a contractive representation of \(L^1(G)\) on \(L^p(G)\). The closure of \(\lambda_p(L^1(G))\) in the operator norm topology of \(B(L^p(G))\) is a Banach algebra, denoted by \(F_\lambda^p(G)\). \textit{E.~Gardella} and \textit{H.~Thiel} have shown in [J. Fourier Anal. Appl. 21, No.~6, 1310--1343 (2015; Zbl 1334.22007)] that the maximal ideal space of \(F_\lambda^p(G)\) is isomorphic to the dual group \(\hat{G}\) of \(G\). In the paper under review, the authors provide another proof to the result.
reviewed by: Yong Zhang
Mathematics Subject Classification ID: 22D20
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 47L10
zbMATH DE Number: 7450626
zbMATH Keywords: commutative Banach algebra
zbMATH Keywords: reduced group \(L^p\)-operator algebra
zbMATH Keywords: maximal ideal space
zbMATH Keywords: Gelfand transformation
MaRDI profile type: Publication
full work available at URL: s43034-021-00160-7
OpenAlex ID: W4200573411
cites work: \(C^*\)-algebras by example
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cites work: Q4520088
cites work: Topological invariants of the maximal ideal space of a Banach algebra
DOI: 10.1007/S43034-021-00160-7
description: scientific article; zbMATH DE number 7450626