Isometries between \(C^ *\)-algebras.
type: Item
instance of: scholarly article
title: Isometries between \(C^ *\)-algebras.
zbMATH Open document ID: 1057.46009
DOI: 10.4171/RMI/381
author: Yanyan Li
published in: Revista Matemática Iberoamericana
publication date: 2004-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/39627
review text: In this important paper, the authors describe into-isometries between \(C^\ast\)-algebras. Given such a map \(T : A \rightarrow B\), there is a largest projection \(p \in B^{\ast\ast}\) such that \(T(.)p : A \rightarrow B^{\ast\ast}\) is a triple homomorphism and \(T\{a,b,c\} = \{Ta,Tb,Tc\}p\) for all \(a,b,c \in A\). When \(A\) is abelian, one also gets \(\| (Ta)p\| = \| a\| \) for all \(a \in A\). This can be seen as an extension of a result of \textit{W. Holsztynski} [Stud. Math. 26 133--136 (1966; Zbl 0156.36903)] that describes into-isometries between continuous function spaces. Of related interest (since in the abelian case isometries are complete isometries) is the work of \textit{D. P. Blecher} and \textit{D. Hay} [``Complete isometries into \(C^\ast\)-algebras'' (Preprint) (2002); see also Contemp. Math. 328, 85--97 (2003; Zbl 1078.46041)]. For further information on the structure of into-isometries, one may consult section 6.4 of the monograph by \textit{R. J. Fleming} and \textit{J. E. Jamison} [``Isometries on Banach spaces: function spaces'' (Monographs and Surveys in Pure and Applied Mathematics 129, Chapman and Hall-CRC, Boca Raton) (2003; Zbl 1011.46001)].
reviewed by: T.S.S.R.K. Rao
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L70
zbMATH DE Number: 2104139
zbMATH Keywords: \(C^\ast\)-algebra
zbMATH Keywords: into-isometry
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2104139