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Abstract

Surjective isometries between unital C*-algebras were classified in 1951 by Kadison \cite{K}. In 1972 Paterson and Sinclair \cite{PS} handled the nonunital case by assuming Kadison's theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon \cite{Y} and the author \cite{S1}, producing a fundamentally new proof of the structure of surjective isometries between (nonunital) C*-algebras. In the final section we indicate how our techniques may be applied to classify surjective isometries of noncommutative $L^p$ spaces, extending the main results of \cite{S1} to $0 < p \leq 1$.