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Compactness and Almost Periodicity of Multipliers

Published online by Cambridge University Press:  20 November 2018

G. Crombez
G. Crombez*
Affiliation:
Seminar of Higher Analysis, State University of GhentGalglaan 2 B-9000 Gent (Belguim)
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Abstract

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The question as to the existence of nontrivial compact or weakly compact multipliers between spaces of functions on groups has been investigated for several years. Until now, however, no general method which is applicable to a large class of function spaces seems to be known

In this paper we prove that the existence of nontrivial compact multipliers between Banach function spaces on which a group acts is related to the existence of nonzero almost periodic functions.

Keywords

43A2243A60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 1 , 01 March 1983 , pp. 58 - 62
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Crombez, G. and Govaerts, W., Compact convolution operators between Lp(G)-spaces, Coll. Math. 39 (1978), 325-329.Google Scholar
2. Crombez, G. and Govaerts, W., Weakly compact convolution operators in L1(G), Simon Stevin 52 (1978), 65-72.Google Scholar
3. Dunford, N. and Schwartz, J. T., Linear operators, part I, New York, Interscience (1958).Google Scholar
4. Dutta, M. and Tewari, B., On multipliers of Segal algebras, Proc. Amer. Math. Soc. 72 (1978), 121-124.Google Scholar
5. Friedberg, S. H., Compact multipliers on Banach algebras, Proc. Amer. Math. Soc. 77 (1979), 210.Google Scholar
6. Kamowitz, H., On compact multipliers of Banach algebras, Proc. Amer. Math. Soc. 81 (1981), 79-80.Google Scholar
7. Krogstad, H. E., Multipliers of Segal algebras, Math. Scand. 38 (1976), 285-303.Google Scholar
8. Lau, A. T., Closed convex invariant subsets of Lp(G) , Trans. Amer. Math. Soc. 232 (1977), 131-142.Google Scholar
9. Loomis, L. H., The spectral characterization of a class of almost periodic functions, Annals of Math. 72 (1960), 362-368.Google Scholar
10. Racher, G., Beispiele von Segalalgebren auf kompakten Gruppen. Preprint.Google Scholar
11. Reiter, H., L1-Algebras and Segal algebras, Springer-Verlag, Berlin (1971).Google Scholar
12. Ylinen, K., Characterizations of B(G) and B(G)∩AP(G) for locally compact groups, Proc. Amer. Math. Soc. 58 (1976), 151-157.Google Scholar