Vol. 24, No. 3, 1968

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On symmetry in certain group algebras

Duane W. Bailey

Vol. 24 (1968), No. 3, 413–419
Abstract

A complex Banach algebra A with involution x x is symmetric if Sp (xx) [0,) for each x A. It is shown that (i) if A is symmetric, the algebra of all n × n matrices with elements from A is symmetric, and (ii) the group algebra of any semi-direct product of a finite group with a locally compact group having a symmetric group algebra is again symmetric.

Mathematical Subject Classification
Primary: 46.60
Milestones
Received: 20 May 1964
Revised: 5 April 1967
Published: 1 March 1968
Authors
Duane W. Bailey