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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

REFERENCES

(0)Bonsall, F. F. and Duncan, J.Complete Wormed algebras. Springer, Ergebnisse der Math. 80 (1973).CrossRefGoogle Scholar
(1)Charpentier, Ph.Q-algébres et produits tensoriels topologiques (Thése, Orsay, 1973).Google Scholar
(2)Chevet, S.Sur certains produits tensoriels topologiques d'espaces de Banach. Z. Wahrscheinlichkeitstheorie und Verw. Gebeite 11 (1969).Google Scholar
(3)Grothendieck, A.Rèsumè de la thèorie mètrique des produits tensoriels topologiques. Bol. Soc. Mat. Sāo Paulo 8 (1956), 1–79.Google Scholar
(4)Kaijser, S.Some remarks on injective Banach algebras (Uppsala University, Depart. Math., Report no. 1975: 10).Google Scholar
(5)Kwapien, N. S.A remark on p-absolutely summing operators in lr-spaces. Studia Math. 34 (1970), 109–111.CrossRefGoogle Scholar
(6)Lindenstrauss, J. and Pelczyński, A.Absolutely summing operators in -spaces and their applications. Studia Math. 29 (1968), 275–326.CrossRefGoogle Scholar
(7)Lindenstrauss, J. and Rosenthal, H. P.The -spaces. Israel J. Math. 7 (1969), 325–349.CrossRefGoogle Scholar
(8)Pietsch, A.Absolut p-summierende Abbildungen in normierten Raümen. Studia Math. 28 (1967), 333–353.CrossRefGoogle Scholar
(9)Saphar, P.Produits tensoriels d'espaces de Banach et classes d'applications linèaires. Studia Math. 38 (1970), 71–100.CrossRefGoogle Scholar
(10)Varopoulos, N. Th.Some remarks on Q-algebras. Ann. Inst. Fourier 22 (1972), 1–11.CrossRefGoogle Scholar
(11)Varopoulos, N. Th.Sur les quotients des algèbres uniformes. C.R. Acad. Sci. Paris 274 (1972),1344–1346.Google Scholar
(12)Varopoulos, N. Th.A theorem on operator algebras. Math. Scand. 37 (1975), 173–182.CrossRefGoogle Scholar
(13)Wermer, J.Quotient algebras of uniform algebras. Symposium on Function Algebras and Rational Approximation, University of Michigan, 1969.CrossRefGoogle Scholar