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• # Artykuł - szczegóły

## Studia Mathematica

2015 | 230 | 3 | 265-279

## Completely bounded lacunary sets for compact non-abelian groups

EN

### Abstrakty

EN
In this paper, we introduce and study the notion of completely bounded $Λ_{p}$ sets ($Λ_{p}^{cb}$ for short) for compact, non-abelian groups G. We characterize $Λ_{p}^{cb}$ 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 $Λ_{p}$ sets for all p < ∞, but are not $Λ_{p}^{cb}$ for any p ≥ 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.

265-279

wydano
2015

### Twórcy

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