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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Isometries of CSL algebras


Author: Baruch Solel
Journal: Trans. Amer. Math. Soc. 332 (1992), 595-606
MSC: Primary 47D25; Secondary 46L10, 46L70
MathSciNet review: 1053117
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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: http://dx.doi.org/10.1090/S0002-9947-1992-1053117-5
PII: S 0002-9947(1992)1053117-5
Keywords: Isometry, Jordan isomorphism, reflexive algebra, CSL, von Neumann algebra, nonselfadjoint algebra
Article copyright: © Copyright 1992 American Mathematical Society