# A new proof of the noncommutative Banach-Stone theorem

Banach Center Publications (2006)

- Volume: 73, Issue: 1, page 363-375
- ISSN: 0137-6934

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topDavid 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 -

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