Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-27T14:27:56.986Z Has data issue: false hasContentIssue false
  • English
  • Français

When is the spectrum of a convolution operator on Lp independent of p?

Published online by Cambridge University Press:  20 January 2009

Bruce A. Barnes
Bruce A. Barnes
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper conditions are given that imply that a convolution operator has the same spectrum on all of the spaces Lp(G), 1≦p≦∞.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 2 , June 1990 , pp. 327 - 332
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

1.Arendt, W., On the o-spectrum of regular operators and the spectrum of measures, Math. Z. 178 (1981), 271–278.Google Scholar
2.Bonsall, F. and Duncan, J., Complete Normed Algebras (Springer-Verlag, Berlin, 1973).CrossRefGoogle Scholar
3.Hulanicki, A., On the spectrum of convolution operators on groups with polynomial growth, Invent. Math. 17 (1972), 135–142.CrossRefGoogle Scholar
4.Jörgens, K., Linear Integral Operators (Pitman, Boston-London-Melbourne, 1982).Google Scholar
5.Pier, J., Amenable Locally Compact Groups (John Wiley & Sons, New York, 1984).Google Scholar
6.Pytlik, T., On the spectral radius of elements in group algebras, Bull. Acad. Polon. Sci. Ser. Sci. Math. 21 (1973), 899–902.Google Scholar
7.Ransford, T., The spectrum of an interpolated operator and analytic multivalued functions, Pacific J. Math. 121 (1986), 445–466.CrossRefGoogle Scholar
8.Rickart, C., Banach Algebras (D. Van Nostrand Co., Princeton, 1960).Google Scholar