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March, 2004 Isometries between C*-algebras
Cho-Ho Chu, Ngai-Ching Wong
Rev. Mat. Iberoamericana 20(1): 87-105 (March, 2004).

Abstract

Let $A$ and $B$ be C*-algebras and let $T$ be a linear isometry from $A$ \emph{into} $B$. We show that there is a largest projection $p$ in $B^{**}$ such that $T(\cdot)p : A \longrightarrow B^{**}$ is a Jordan triple homomorphism and $$ T(a b^* c + c b^* a) p= T(a) T(b)^* T(c) p + T(c) T(b)^* T(a) p $$ for all $a$, $b$, $c$ in $A$. When $A$ is abelian, we have $\|T(a)p\|=\|a\|$ for all $a$ in $A$. It follows that a (possibly non-surjective) linear isometry between any C*-algebras reduces {\it locally} to a Jordan triple isomorphism, by a projection.

Citation

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Cho-Ho Chu. Ngai-Ching Wong. "Isometries between C*-algebras." Rev. Mat. Iberoamericana 20 (1) 87 - 105, March, 2004.

Information

Published: March, 2004
First available in Project Euclid: 2 April 2004

zbMATH: 1057.46009
MathSciNet: MR2069021

Subjects:
Primary: 32M15 , 46B04 , 46L05 , 46L70

Keywords: Banach manifold , C*-algebra , isometry , JB*-triple

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

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