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Sets of p-multiplicity in locally compact groups

I. G. Todorov; L. Turowska — 2015

Studia Mathematica

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 $E * = (s, t) : t s^{- 1} \in E$ 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.

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