Hostname: page-component-7857688df4-8r446 Total loading time: 0 Render date: 2025-11-19T11:02:40.021Z Has data issue: false hasContentIssue false
  • English
  • Français

Logarithms in multiplier algebras

Published online by Cambridge University Press:  20 January 2009

G. V. Wood
G. V. Wood
Affiliation:
Department of Pure Mathematics, University College of Swansea, Singleton Park, Swansea, SA2 8PP
Rights & Permissions [Opens in a new window]

Extract

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 (3) it is shown that, for a locally compact abelian group G and x∈G, δx has a logarithm in M(G) if and only if x has finite order. Since M(G) can be identified with the multipliers of L1(G), one might expect a similar result for the algebras of multipliers on Lp(G) for 1 < p < ∞. However, in contrast, it is shown in (2) that for a locally compact abelian group G and 1 < p < ∞, every translation operator on Lp(G) has a logarithm in the multiplier algebra. Here we consider whether the same results are true for non-abelian groups.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 3 , October 1979 , pp. 187 - 190
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1) Bredon, , Introduction to compact transformation groups (Academic Press, 1972).Google Scholar
(2) Gillespie, T. A., Logarithms of L p translations, Indiana Univ. M. J. 24 (1975), 1037–1045.CrossRefGoogle Scholar
(3) Gillespie, T. A., and West, T. T., Weakly compact groups of operators, Proc. Amer.Math. Soc. 49 (1975), 78–82.CrossRefGoogle Scholar
(4) Herz, C., Harmonic synthesis for subgroups, Ann. Inst. Fourier 23, 3 (1973), 91–123.CrossRefGoogle Scholar
(5) Hewitt, and Ross, , Abstract Harmonic Analysis, vol. I and II, (Springer-Verlag, 1963 and 1970).Google Scholar
(6) Taylor, J. L., Measure algebras, CBMS No. 16, (1973)Google Scholar