# Isometries between C*-algebras

### Cho-Ho J. Chu

Queen Mary University, London, UK### Ngai-Ching Wong

National Sun Yet-sen University, Kaohsiung, Taiwan

## 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.

## Cite this article

Cho-Ho J. Chu, Ngai-Ching Wong, Isometries between C*-algebras. Rev. Mat. Iberoam. 20 (2004), no. 1, pp. 87–105

DOI 10.4171/RMI/381