Isometric isomorphisms in proper \(CQ^*\)-algebras
type: Item
instance of: scholarly article
title: Isometric isomorphisms in proper \(CQ^*\)-algebras
zbMATH Open document ID: 1175.39025
author: Choonkil Park
author: Jong Su An
publication date: 2009-09-03T00:00:00Z
review text: Let \(A\) be a Banach module over a \(C^*\)-algebra \(A_0\) with involution \(*\) and \(C^*\)-norm \(\|.\|_0\) such that \(A_0\subseteq A\). We say that \((A,A_0)\) is a proper \(CQ^*\)-algebra if (i) \(A_0\) is dense in \(A\) with respect to its norm \(\|.\|;\) (ii) An involution \(*\) which extends the involution of \(A_0\), is defined in \(A\) with the property \((xy)^*=y^*x^*\) for all \(x,y\in A\) whenever the multiplication is defined; (iii)\(\|y\|_0= \sup_{x\in A, \|x\|\leq 1}\|xy\|\) for all \(y\in A_0.\) In this paper the authors investigate the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper \(CQ^*\)-algebras for the Cauchy-Jensen additive mapping \[ 2f(\frac{x_1+x_2}{2}+y)=f(x_1)+f(x_2)+2f(y). \]
reviewed by: Maryam Amyari
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 5601609
zbMATH Keywords: Cauchy-Jensen functional equation
zbMATH Keywords: Hyers-Ulam-Rassias stability
zbMATH Keywords: isometric isomorphism in proper \(CQ^*\)-algebras
MaRDI profile type: Publication
full work available at URL: s10114-009-7454-7
OpenAlex ID: W2080268442
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DOI: 10.1007/S10114-009-7454-7
published in: Acta Mathematica Sinica, English Series
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description: scientific article; zbMATH DE number 5601609