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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On symmetry of Banach Jordan algebras


Authors: B. Aupetit and M. A. Youngson
Journal: Proc. Amer. Math. Soc. 91 (1984), 364-366
MSC: Primary 46H70; Secondary 17C65, 46K05
MathSciNet review: 744630
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0744630-7
PII: S 0002-9939(1984)0744630-7
Keywords: Banach Jordan algebra, spectrum, spectral radius, subharmonic function, $ J{B^ * }$-algebra
Article copyright: © Copyright 1984 American Mathematical Society