Completely bounded lacunary sets for compact non-abelian groups

Kathryn Hare ¹   ; Parasar Mohanty ²

¹ Department of Pure Mathematics University of Waterloo 200 University Avenue West Waterloo, Ontario, Canada N2L 3G1
² Department of Mathematics and Statistics Indian Institute of Technology Kanpur, U.P., 208016, India

Studia Mathematica, Tome 230 (2015) no. 3, pp. 265-279

Résumé

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.

Détail

DOI : 10.4064/sm8391-1-2016

Keywords: paper introduce study notion completely bounded varlambda sets varlambda short compact non abelian groups characterize varlambda sets terms completely bounded multipliers prove infinite product special unitary groups arbitrarily large dimension there sets consisting representations unbounded degree varlambda sets infty varlambda geq done showing space completely bounded multipliers proper subset space multipliers