Vol. 31, No. 3, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
Noncommutative convolution measure algebras

Joseph L. Taylor

Vol. 31 (1969), No. 3, 809–826

A convolution measure algebra is a partially ordered Banach algebra in which the norm, order, and algebraic operations are related in special ways. Examples include the group algebra L1(G) and measure algebra M(G) on a locally compact group G and, more generally, the measure algebra M(S) on any locally compact semigroup S.

This paper demonstrates several ways in which a convolution measure algebra can be realized as an algebra of measures on a compact semigroup. A relationship is established between such realizations and certain classes of Banach space representations of the algebra. These results give a partial extension to the noncommutative case of the structure theory of commutative semi-simple convolution measure algebras.

Mathematical Subject Classification
Primary: 46.80
Received: 25 October 1966
Revised: 2 June 1969
Published: 1 December 1969
Joseph L. Taylor