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Sets of synthesis for general algebras

Published online by Cambridge University Press:  24 October 2008

T. W. Körner
T. W. Körner
Affiliation:
Trinity Hall, Cambridge
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Abstract

Following a program of Reiter, sets of synthesis in Banach algebras with certain Ditkin conditions are discussed. It is shown that the Ditkin Shilov lemma is in a general context best possible. Various methods for the construction of algebras are discussed. These are applied to show that very strong homogeneity conditions are needed to ensure that star sets are of synthesis for regular Ditkin algebras with Rn as carrier space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 3 , May 1970 , pp. 559 - 568
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Hoffman, K.Banach spaces of analytic functions (Prentice Hall, New Jersey, 1962).Google Scholar
(2)Kahane, J.-P. and Salem, R.Ensembles parfaits et séries trigonométriques (Hermann, Paris, 1963).Google Scholar
(3)Katznelson, Y.An introduction to harmonic analysis (John Wiley and Sons, New York, 1968).Google Scholar
(4)Loomis, L. H.An introduction to harmonic analysis (Van Nostrand, New Jersey, 1953).Google Scholar
(5)Reiter, H.Classical harmonic analysis and locally compact groups (Oxford, 1968).Google Scholar
(6)Rudin, W.Fourier analysis on groups (John Wiley and Sons, New York, 1967).Google Scholar