A new proof of the noncommutative Banach-Stone theorem

2004/09/24 by David Sherman, Sherman, David · 1 citation
Mathematics · #46B04 #46L05 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46B04 #msc:46L05

paper · pdf · doi:10.48550/arxiv.math/0409488

12 pages

arxiv created 2004/09/24 · arxiv updated 2009/12/01

Abstract

Surjective isometries between unital C*-algebras were classified in 1951 by Kadison. In 1972 Paterson and Sinclair 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 and the author, 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 Lp spaces, extending some recent results of the author to 0 < p leq 1.

Cited by

• On preservers of strong Birkhoff-James orthogonality between C^*-algebras

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