Vol. 31, No. 3, 1969

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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