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Transactions of the American Mathematical Society

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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.

References [Enhancements On Off] (What's this?)

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Keywords: Isometry, Jordan isomorphism, reflexive algebra, CSL, von Neumann algebra, nonselfadjoint algebra
Article copyright: © Copyright 1992 American Mathematical Society

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