Real Banach \(*\) algebras
type: Item
instance of: scholarly article
title: Real Banach \(*\) algebras
zbMATH Open document ID: 0977.46033
author: Bingren Li
author: Ping-Kwan Tam
publication date: 2002-01-07T00:00:00Z
review text: The systematic study of real Banach *-algebras are given in this paper. It is shown that \textit{J. W. M. Ford}'s lemma [see J. Lond. Math. Soc. 42, 521-522 (1967; Zbl 0145.38702)] and \textit{V. Pták}'s inequality [see Bull. Lond. Math. Soc. 2, 327-334 (1970; Zbl 0209.44403)] hold in the real case and the (real) linear span of unitary elements contains all skew-hermitian elements. Moreover, main properties of symmetric real Banach *-algebras, of *-representations and topologically irreducible *-representations of real Banach *-algebras, of *-radical of real Banach *-algebras, of the enveloping real \(C^*\)-algebras of a hermitian real Banach *-algebra and of the real state space of a hermitian real Banach*-algebra without identity are described.
reviewed by: Mati Abel
Mathematics Subject Classification ID: 46K05
Mathematics Subject Classification ID: 46K10
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46H05
zbMATH DE Number: 1530092
zbMATH Keywords: real Banach *-algebras
zbMATH Keywords: *-representations
zbMATH Keywords: *-radical
zbMATH Keywords: Symmetric real Banach algebras
zbMATH Keywords: enveloping real \(C^*\)-algebras
MaRDI profile type: Publication
full work available at URL: s101140000062
OpenAlex ID: W1991324912
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DOI: 10.1007/S101140000062
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1530092