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Bipositive and Isometric Isomorphisms of Some Convolution Algebras

Published online by Cambridge University Press:  20 November 2018

R. E. Edwards
R. E. Edwards*
Affiliation:
Institute of Advanced Studies, Australian National University
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Throughout this paper the term "space" will mean "Hausdorff locally compact space" and the term '"group" will mean "Hausdorff locally compact group." If G is a group and 1 ≤ p < ∞, Lp(G) denotes the usual Lebesgue space formed relative to left Haar measure on G. It is well known that L1(G) is an algebra under convolution, and that the same is true of Lp(G) whenever G is compact. We introduce also the space Cc(G) of complex-valued continuous functions f on G for each of which the support (supp f), is compact. The "natural" topology of CC(G) is obtained by regarding CC(G) as the inductive limit of its subspaces

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 839 - 846
Copyright
Copyright © Canadian Mathematical Society 1965

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