Isometries of CSL algebras

Author:
Baruch Solel

Journal:
Trans. Amer. Math. Soc. **332** (1992), 595-606

MSC:
Primary 47D25; Secondary 46L10, 46L70

DOI:
https://doi.org/10.1090/S0002-9947-1992-1053117-5

MathSciNet review:
1053117

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that every Jordan isomorphism of CSL algebras, whose restriction to the diagonal of the algebra is a selfadjoint map, is the sum of an isomorphism and an anti-isomorphism.

It follows that every surjective linear isometry of CSL algebras is the sum of an isomorphism and an anti-isomorphism, followed by a unitary multiplication.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1053117-5

Keywords:
Isometry,
Jordan isomorphism,
reflexive algebra,
CSL,
von Neumann algebra,
nonselfadjoint algebra

Article copyright:
© Copyright 1992
American Mathematical Society