p-Pseudomeasures and closed subgroups |
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Authors: | Jacques Delaporte Antoine Derighetti |
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Institution: | (1) Institut de Mathématiques Faculté des Sciences, Université de Lausanne, CH-1015 Lausanne-Dorigny, Switzerland |
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Abstract: | LetPM
p
(G) be the space of allp-pseudomeasures on a locally compact groupG. We show the existence of a conditional expectation fromPM
p
(G) ontoPM
p
(H) whereH is a closed normal subgroup ofG. As an application we give a new proof of the fact thatH is a set ofp-synthesis inG; we also get an inequality involving the operator norm of bounded measures onG. Moreover, in analogy with a theorem of Reiter, we obtain a result concerning the closed ideals of the Figà-Talamanca Herz algebra ofG. |
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Keywords: | 43A15 |
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