a1 Carleton University, Ottawa, Canada.
Let A1, A2 be Banach algebras, A1 A2 their algebraic tensor product over the complex field. If · α is an algebra norm on A1 A2 we write A1 α A2 for the · α-completion of A1 A2. In this note we study the existence of identities and approximate identities in A1 α 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)