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Sets of $p$-multiplicity in locally compact groups

Volume 226 / 2015

I. G. Todorov, L. Turowska Studia Mathematica 226 (2015), 75-93 MSC: Primary 47L05; Secondary 43A46, 22D25 DOI: 10.4064/sm226-1-4

Abstract

We initiate the study of sets of $p$-multiplicity in locally compact groups and their operator versions. We show that a closed subset $E$ of a second countable locally compact group $G$ is a set of $p$-multiplicity if and only if $E^* = \{(s,t) : ts^{-1}\in E\}$ is a set of operator $p$-multiplicity. We exhibit examples of sets of $p$-multiplicity, establish preservation properties for unions and direct products, and prove a $p$-version of the Stone–von Neumann Theorem.

Authors

  • I. G. TodorovPure Mathematics Research Centre
    Queen's University Belfast
    Belfast BT7 1NN, United Kingdom
    e-mail
  • L. TurowskaDepartment of Mathematical Sciences
    Chalmers University of Technology and
    the University of Gothenburg
    Gothenburg SE-412 96, Sweden
    e-mail

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