Vol. 32, No. 1, 1970

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ISSN: 0030-8730
Symmetry and nonsymmetry in the group algebras of discrete groups

Joe W. Jenkins

Vol. 32 (1970), No. 1, 131–145

A Banach *-algebra 𝒰, with identity e, is symmetric if xx + e is regular for each x in 𝒰. In this paper we generalize certain conditions on a discrete group G that are known to be sufficient to ensure symmetry of l1(G). Also we define semi-symmetry and derive an inequality that must be satisfied if l1(G) is not semi-symmetric. Finally we show that if a group contains a free subsemigroup on two or more generators then l1(G) is not symmetric.

Mathematical Subject Classification
Primary: 46.80
Received: 3 February 1969
Published: 1 January 1970
Joe W. Jenkins