Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T02:28:13.190Z Has data issue: false hasContentIssue false
  • English
  • Français

Two results on very strongly homogeneous algebras

Published online by Cambridge University Press:  24 October 2008

T. W. Körner
T. W. Körner
Affiliation:
Trinity Hall, Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that under quite general circumstances a Banach algebra R need not be closed in its tilda algebra . In answer to a query of Katznelson we show that there is a very strongly homogeneous algebra B ≠ C0(R) on R with R as carrier space such that non-analytic functions operate on B.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 2 , September 1970 , pp. 363 - 376
Copyright
Copyright © Cambridge Philosophical Society 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Körner, T. W.Sets of synthesis for general algebras. Proc. Cambridge Philos. Soc. (in the Press).Google Scholar
(2)Varopoulos, N.-Th.On a problem of A. Beurling. J. Functional Analysis 2 (1968), 24–30.CrossRefGoogle Scholar
(3)Katznelson, Y.An introduction to harmonic analysis (John Wiley and Sons, New York, 1968).Google Scholar
(4)Rudin, W.Fourier analysis on groups (John Wiley and Sons, New York, 1967).Google Scholar
(5)Katznelson, Y.Calcul symbolique dans les algèbres homogènes. C.R. Acad. Sci. Paris 254 (1962), 2700.Google Scholar
(6)Rudin, W.Real and complex analysis (McGraw-Hill, New York, 1966).Google Scholar
(7)Saks, S.Theory of the integral, vol. vii (Monograf je Matematyczne, Warszawa-Lwow, 1937).Google Scholar