Finding a maximal subalgebra on which the two Arens products agree

Julien O. Hennefeld

Vol. 59 (1975), No. 1, 93–98

DOI: 10.2140/pjm.1975.59.93

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