Vol. 17, No. 1, 1966

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The bidual of a locally multiplicatively-convex algebra

Sidney (Denny) L. Gulick

Vol. 17 (1966), No. 1, 71–96

This paper combines two extensions of the theory of Banach algebras. On the one hand, Arens and Michael generalized the theory of Banach algebras by introducing the concept of a locally multiplicatively-convex topological algebra (abbreviated “lmc” algebra). On the other hand, Arens gave a procedure for defining on the bidual (the second topological conjugate space) of a Banach algebra a multiplication which makes the bidual also into a Banach algebra. We show that one can put an Arens multiplication onto the bidual of an lmc algebra, and we study the algebraic and topological properties of the bidual when it is endowed with such a multiplication.

Mathematical Subject Classification
Primary: 46.50
Received: 7 November 1963
Revised: 16 June 1964
Published: 1 April 1966
Sidney (Denny) L. Gulick