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Local spectral properties of convolution operators on non-abelian groups

Published online by Cambridge University Press:  20 January 2009

Volker Runde
Volker Runde
Affiliation:
Fachbereich 9 Mathematik Universität Des Saarlandes Postfach 151150 66041 Saarbrücken Germany E-mail address: runde@math.uni-sb.de
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Abstract

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Let G be a Moore group. Then, for each f∈L1(G), the convolution operator Lf: L1(G)→L1(G) is decomposable. On the other hand, there is a discrete probability measure µ on a compact group G such that Lµ: Ll(G)→Ll(G) fails to be decomposable.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 1 , February 1996 , pp. 143 - 149
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Akemann, C. A., Some mapping properties of the group algebras of a compact group, Pacific J. Math. 22 (1967), 1–8.CrossRefGoogle Scholar
2. Albrecht, E., Decomposable systems of operators in harmonic analysis, in Toeplitz Centennial (Gohberg, I., ed, Birkhäuser, 1982), pp. 13–37.Google Scholar
3. Albrecht, E. and Mehta, R. D., Some remarks on local spectral theory, J. Operator Theory 12(1984), 285–317.Google Scholar
4. Barnes, B. A., The properties *-regularity and uniqueness of C*-norm in a general *-algebra, Trans. Amer. Math. Soc. 279 (1983), 841–859.Google Scholar
5. Colojoară, I. and Foiaş, C., Theory of Generalized Spectral Operators (Gordon and Breach, 1968).Google Scholar
6. Dixmier, J., Opérateurs de rang fmi dans les représentations unitaires, Publ. Math. I.H.E.S. 6 (1960), 13–25.CrossRefGoogle Scholar
7. Eschmeier, J., Operator decomposability and weakly continuous representations of locally compact abelian groups, J. Operator Theory 7 (1982), 201–208.Google Scholar
8. Figà-Talamanca, A. and Picardello, M. A., Harmonic Analysis on Free Groups (Marcel Dekker, 1983).Google Scholar
9. Grosser, S. and Moskowitz, M., On central topological groups, Trans. Amer. Math. Soc. 127 (1967), 317–340.CrossRefGoogle Scholar
10. Grosser, S. and Moskowitz, M., Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1–40.Google Scholar
11. Hauenschild, W. and Kaniuth, E., The generalized Wiener theorem for groups with finite-dimensional representations, J. Fund. Anal. 31 (1979), 13–23.CrossRefGoogle Scholar
12. Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis, I (Springer Verlag, 1963).Google Scholar
13. Laursen, K. B. and Neumann, M. M., Decomposable operators and automatic continuity, J. Operator Theory 15 (1986), 33–51.Google Scholar
14. Laursen, K. B. and Neumann, M. M., Decomposable multipliers and applications to harmonic analysis, Studio Math. 101 (1992), 193–214.CrossRefGoogle Scholar
15. Laursen, K. B. and Neumann, M. M., Asymptotic intertwining and spectral inclusions on Banach spaces, Czechoslovak Math. J. 43 (1993), 483–497.CrossRefGoogle Scholar
16. Liukkonen, J. and Mosak, R. D., Harmonic analysis and centers of group algebras, Trans. Amer. Math. Soc. 195 (1974), 147–163.CrossRefGoogle Scholar
17. Mosak, R. D., The Ll- and C*-algebras of -groups and their representations, Trans. Amer. Math. Soc. 163 (1972), 277–310.Google Scholar
18. Palmer, T. W., Classes of nonabelian, noncompact, locally compact groups, Rocky Mountain J. Math. 8 (1978), 681–741.CrossRefGoogle Scholar
19. Paterson, A. T., Amenability (American Mathematical Society, 1988).CrossRefGoogle Scholar
20. Robertson, L. C., A note on the structure of Moore groups, Bull. Amer. Math. Soc. 75 (1969), 594–599.CrossRefGoogle Scholar
21. Runde, V., Homomorphisms from L1(G) for G∈[FIA]- ∪ [Moore], J. Fund. Anal. 122 (1994), 25–51.CrossRefGoogle Scholar
22. Runde, V., Intertwining operators over L1(G) for G ∈[PG]∩[SIN], Math. Z., to appear.Google Scholar