Vol. 59, No. 1, 1975

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Finding a maximal subalgebra on which the two Arens products agree

Julien O. Hennefeld

Vol. 59 (1975), No. 1, 93–98
Abstract

Arens has given two ways of defining a Banach algebra product on the second dual of a Banach algebra 𝒜. In this paper we give a construction for finding a maximal subalgebra on which the two Arens products agree. Moreover, we give an example which shows that there is not necessarily a unique maximal subalgebra on which the two Arens products agree. This example is a Banach algebra whose second dual has a nonunique element I which is simultaneously a right identity under the first Arens product and a left identity under the second Arens product.

Mathematical Subject Classification 2000
Primary: 46H05
Milestones
Received: 10 September 1974
Published: 1 July 1975
Authors
Julien O. Hennefeld