Bipositive and Isometric Isomorphisms of Some Convolution Algebras
- 1 January 1965
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 17, 839-846
- https://doi.org/10.4153/cjm-1965-082-8
Abstract
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 subspacesKeywords
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