A new proof of the noncommutative Banach-Stone theorem

• Autorzy: David Sherman
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L05: General theory of C * -algebras
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 73
• Numer: 1
• Strony: 363-375

Daty

wydano

2006

Twórcy

autor

David Sherman

• Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.

Identyfikatory

DOI

10.4064/bc73-0-29