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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the symmetry of matrix algebras

Author: Josef Wichmann
Journal: Proc. Amer. Math. Soc. 54 (1976), 237-240
MathSciNet review: 0388110
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Abstract: A $ ^{\ast}$-algebra is called symmetric, if each element of the form $ {a^{\ast}}a$ has nonnegative real spectrum. The study of locally compact groups with symmetric group algebras led to the following theorem: The tensoring of a Banach $ ^{\ast}$-algebra with the $ ^{\ast}$-algebra of all complex $ n \times n$ matrices preserves symmetry. In this note we prove, by a very simple algebraic argument, an analogue of it for arbitrary $ ^{\ast}$-algebras.

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Keywords: Matrix algebra, $ ^{\ast}$-algebra, group algebra, symmetry
Article copyright: © Copyright 1976 American Mathematical Society