Revista Matemática Iberoamericana

Isometries between C*-algebras

Cho-Ho Chu and Ngai-Ching Wong

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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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 20, Number 1 (2004), 87-105.

Dates
First available in Project Euclid: 2 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1080928421

Mathematical Reviews number (MathSciNet)
MR2069021

Zentralblatt MATH identifier
1057.46009

Subjects
Primary: 46L05: General theory of $C^*$-algebras 46B04: Isometric theory of Banach spaces 46L70: Nonassociative selfadjoint operator algebras [See also 46H70, 46K70] 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]

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

Citation

Chu, Cho-Ho; Wong, Ngai-Ching. Isometries between C*-algebras. Rev. Mat. Iberoamericana 20 (2004), no. 1, 87--105. https://projecteuclid.org/euclid.rmi/1080928421


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