A new proof of the noncommutative Banach-Stone theorem

David Sherman. "A new proof of the noncommutative Banach-Stone theorem." Banach Center Publications 73.1 (2006): 363-375. <http://eudml.org/doc/281653>.

@article{DavidSherman2006,
abstract = {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 $L^p$ spaces, extending the main results of [S1] to 0 < p ≤ 1.},
author = {David Sherman},
journal = {Banach Center Publications},
keywords = {-algebras; surjective isometries; Jordan isomorphism},
language = {eng},
number = {1},
pages = {363-375},
title = {A new proof of the noncommutative Banach-Stone theorem},
url = {http://eudml.org/doc/281653},
volume = {73},
year = {2006},
}

TY - JOUR
AU - David Sherman
TI - A new proof of the noncommutative Banach-Stone theorem
JO - Banach Center Publications
PY - 2006
VL - 73
IS - 1
SP - 363
EP - 375
AB - 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 $L^p$ spaces, extending the main results of [S1] to 0 < p ≤ 1.
LA - eng
KW - -algebras; surjective isometries; Jordan isomorphism
UR - http://eudml.org/doc/281653
ER -