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Representation theory for tensor products of Banach algebras

Published online by Cambridge University Press:  24 October 2008

T. K. Carne
T. K. Carne
Affiliation:
Trinity College, Cambridge
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Extract

The algebraic tensor product A1⊗A2 of two Banach algebras is an algebra in a natural way. There are certain norms α on this tensor product for which the multiplication is continuous so that the completion, A1αA2, is a Banach algebra. The representation theory of such tensor products is the subject of this paper. It will be shown that, under certain simple conditions, the tensor product of two semi-simple Banach algebras is semi-simple although, without these conditions, the result fails.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 3 , November 1981 , pp. 445 - 463
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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