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The predual of the space of convolutors on a locally compact group

Published online by Cambridge University Press:  17 April 2009

Michael Cowling
Michael Cowling
Affiliation:
School of MathematicsUniversity of New South Wales, Sydney NSW 2052Australia, e-mail: [email protected]
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Abstract

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Let Cvp(G) be the space of convolution operators on the Lebesgue space LP(G), for an arbitrary locally compact group G. We describe Cvp(G) as a dual space, whose predual, is a Banach algebra of functions on G, under pointwise operations, with maximal ideal space G. This involves a variation of Herz's definition of AP(G); the benefit of this new definition is that all of Cvp(G) is obtained as the dual in the nonamenable setting. We also discuss further developments of this idea.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 409 - 414
Copyright
Copyright © Australian Mathematical Society 1998

References

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