Bulletin of the Australian Mathematical Society

Table of Contents - April 1970 - Volume 2, Issue 02  

Research Article

Identities in tensor products of Banach algebras

R. J. Loya1

a1 Carleton University, Ottawa, Canada.

Abstract

Let A1, A2 be Banach algebras, A1 xs2297 A2 their algebraic tensor product over the complex field. If xs2016 · xs2016α is an algebra norm on A1 xs2297 A2 we write A1 xs2297α A2 for the xs2016 · xs2016α-completion of A1 xs2297 A2. In this note we study the existence of identities and approximate identities in A1 xs2297α A2 versus their existence in A1 and A2. Some of the results obtained are already known, but our method of proof appears new, though it is quite elementary.

(Received January 10 1970)