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Identities in tensor products of Banach algebras

Published online by Cambridge University Press:  17 April 2009

R. J. Loy
R. J. Loy
Affiliation:
Carleton University, Ottawa, Canada.
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Abstract

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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 ⊗αA2 for the ‖ · ‖α-completion of A1 ⊗ A2. In this note we study the existence of identities and approximate identities in A1 ⊗αA2 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 2 , April 1970 , pp. 253 - 260
Copyright
Copyright © Australian Mathematical Society 1970

References

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