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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
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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.

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

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