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p-Pseudomeasures and closed subgroups

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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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  1. Institut de Mathématiques Faculté des Sciences, Université de Lausanne, CH-1015, Lausanne-Dorigny, Switzerland

    Jacques Delaporte & Antoine Derighetti

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  1. Jacques Delaporte
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  2. Antoine Derighetti
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Delaporte, J., Derighetti, A. p-Pseudomeasures and closed subgroups. Monatshefte für Mathematik 119, 37–47 (1995). https://doi.org/10.1007/BF01292767

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  • DOI: https://doi.org/10.1007/BF01292767

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