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The ~ -representations of symmetric homogeneous algebras

Published online by Cambridge University Press:  09 April 2009

J. A. Ward
Affiliation:
School of Mathematical and Physical Sciences, Murdoch University, Murdoch, Western Australia 6155, Australia
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Abstract

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In 1947 I. E. Segal proved that to each non-degenerate ~ -representation R of L1 (= L1 (G) for a compact group G) with representation space , there corresponds a continuous unitary representation W of G, also with representation space , which satisfies

for each fL1 and hk . This was extended to Lp,1 p < , in 1970 by E. Hewitt and K. A. Ross. We now generalize this result to any symmetric homogeneous convolution Banach alebra of pseudomeasures on G. Further we prove that the correspondence preserves irreduibility.

Type
Research Article
Copyright
Copyright Australian Mathematical Society 1986

References

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