Sets of $p$-multiplicity in locally compact groups
Volume 226 / 2015
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.
