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Not all H′-algebras are operator algebras

Published online by Cambridge University Press:  24 October 2008

T. K. Carne
T. K. Carne
Affiliation:
Trinity College, Cambridge, CB2 1TQ
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Extract

An H′-algebra which is not an operator algebra is constructed. This is used to prove that the class of operator algebras is not equal to the class of α-algebras for any tensor norm α.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 2 , September 1979 , pp. 243 - 250
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Carne, T. K.Tensor products and Banach algebras. J. London Math. Soc. 17 (1978), 480–488.CrossRefGoogle Scholar
(2)Charpentier, PH. Q-algèbres et produits tensoriels topologiques. Thèse, Orsay (1973).Google Scholar
(3)Grothendieck, A.Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. São Paulo 8 (1956), 1–79.Google Scholar
(4)Sakai, S.C*-algebras and W*-algebras (Berlin, Heidelberg, New York, Springer-Verlag, 1971).Google Scholar
(5)Tonge, A. M.Banach algebras and absolutely summing operators. Proc. Cambridge Philos. Soc. 80,(1976), 465–473.CrossRefGoogle Scholar
(6)Varopoulos, N. Th.A theorem on operator algebras. Math. Scand. 37 (1975), 173–182.CrossRefGoogle Scholar
(7)Varopoulos, N. Th.Sur une inégalitéde von Neumann. C. R. Acad. Sci. Paris A 277 (1973), 19–22.Google Scholar