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Completely bounded lacunary sets for compact non-abelian groups

Volume 230 / 2015

Kathryn Hare, Parasar Mohanty Studia Mathematica 230 (2015), 265-279 MSC: Primary 43A46; Secondary 46L07, 47L25. DOI: 10.4064/sm8391-1-2016 Published online: 27 January 2016

Abstract

In this paper, we introduce and study the notion of completely bounded $\varLambda _{p}$ sets ($\varLambda _{p}^{\rm cb}$ for short) for compact, non-abelian groups $G$. We characterize $\varLambda _{p}^{\rm cb}$ sets in terms of completely bounded $L^{p}(G)$ multipliers. We prove that when $G$ is an infinite product of special unitary groups of arbitrarily large dimension, there are sets consisting of representations of unbounded degree that are $\varLambda _{p} $ sets for all $p \lt \infty $, but are not $\varLambda _{p}^{\rm cb}$ for any $p\geq 4$. This is done by showing that the space of completely bounded $L^{p}(G)$ multipliers is a proper subset of the space of $L^{p}(G)$ multipliers.

Authors

  • Kathryn HareDepartment of Pure Mathematics
    University of Waterloo
    200 University Avenue West
    Waterloo, Ontario, Canada N2L 3G1
    e-mail
  • Parasar MohantyDepartment of Mathematics and Statistics
    Indian Institute of Technology
    Kanpur, U.P., 208016, India
    e-mail

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