Completely bounded lacunary sets for compact non-abelian groups

• Autorzy: Kathryn Hare , Parasar Mohanty
• Języki publikacji: 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.

Kategorie tematyczne

• 46L07: Operator spaces and completely bounded maps
• 47L25: Operator spaces (= matricially normed spaces)
• 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 230
• Numer: 3
• Strony: 265-279

Daty

wydano

2015

Twórcy

autor

Kathryn Hare

• Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1

autor

Parasar Mohanty

• Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, U.P., 208016, India

Identyfikatory

DOI

10.4064/sm8391-1-2016