Completely bounded lacunary sets for compact non-abelian groups

Kathryn Hare, and Parasar Mohanty. "Completely bounded lacunary sets for compact non-abelian groups." Studia Mathematica 230.3 (2015): 265-279. <http://eudml.org/doc/285615>.

@article{KathrynHare2015,
abstract = {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.},
author = {Kathryn Hare, Parasar Mohanty},
journal = {Studia Mathematica},
keywords = {lacunary set; completely bounded multiplier; sidon set},
language = {eng},
number = {3},
pages = {265-279},
title = {Completely bounded lacunary sets for compact non-abelian groups},
url = {http://eudml.org/doc/285615},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Kathryn Hare
AU - Parasar Mohanty
TI - Completely bounded lacunary sets for compact non-abelian groups
JO - Studia Mathematica
PY - 2015
VL - 230
IS - 3
SP - 265
EP - 279
AB - 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.
LA - eng
KW - lacunary set; completely bounded multiplier; sidon set
UR - http://eudml.org/doc/285615
ER -