Vol. 34, No. 1, 1970

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On a class of topological algebras

Allan C. Cochran, R. Keown and C. R. Williams

Vol. 34 (1970), No. 1, 17–25

This note introduces a class of topological algebras, called A-convex, which generalize the notion of locally m-convex algebras. They include a number of function space algebras which are not locally m-convex. Certain of these algebras admit a modified Gel’fand type representation in a space of vector-valued functions without invoking commutativity requirements. One seemingly obtains a new way of representing locally m-convex algebras. A-convex algebras are locally m-convex under the assumption of completeness of certain factor algebras in a suitable topology.

Mathematical Subject Classification
Primary: 46.50
Received: 21 May 1969
Published: 1 July 1970
Allan C. Cochran
R. Keown
C. R. Williams