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Banach algebras and absolutely summing operators

Published online by Cambridge University Press:  24 October 2008

Andrew M. Tonge
Andrew M. Tonge
Affiliation:
Université de Paris-Sud, Orsay
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Extract

If R is a Banach algebra and ø ∈ R′, the dual space, then we may define a bounded linear map by

We shall show that for suitable p the requirement that each be p-absolutely summing constrains R to be an operator algebra, or even, in certain cases, a uniform algebra. In this way we are able to give generalizations of results of Varopoulos (12) and Kaijser (4).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 3 , November 1976 , pp. 465 - 473
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

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