Vol. 32, No. 1, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
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