On symmetry of Banach Jordan algebras

Aupetit, B.; Youngson, M. A.

doi:10.1090/S0002-9939-1984-0744630-7

On symmetry of Banach Jordan algebras
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by B. Aupetit and M. A. Youngson PDF

Proc. Amer. Math. Soc. 91 (1984), 364-366 Request permission

Abstract:

Using a very simple subharmonic argument we prove that a Banach Jordan algebra is Hermitian if and only if the sum of two positive elements is positive. We apply this result to give a characterization of Banach Jordan algebras with involution which are $J{B^ * }$-algebras for an equivalent norm.

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