Isometries of CSL algebras

Solel, Baruch

doi:10.1090/S0002-9947-1992-1053117-5

Isometries of CSL algebras
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Trans. Amer. Math. Soc. 332 (1992), 595-606 Request permission

Abstract:

We show that every Jordan isomorphism of $\text {CSL}$ 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 $\text {CSL}$ algebras is the sum of an isomorphism and an anti-isomorphism, followed by a unitary multiplication.

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Isometries of certain reflexive operator algebras