Surjective isometries between unital C*-algebras were classified in 1951 by Kadison [K]. In 1972 Paterson and Sinclair [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 [Y] and the author [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 spaces, extending the main results of [S1] to 0 < p ≤ 1.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-29,
author = {David Sherman},
title = {A new proof of the noncommutative Banach-Stone theorem},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {363-375},
zbl = {1112.46010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-29}
}
David Sherman. A new proof of the noncommutative Banach-Stone theorem. Banach Center Publications, Tome 72 (2006) pp. 363-375. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-29/