Completely bounded lacunary sets for compact non-abelian groups

Kathryn Hare; Parasar Mohanty

Studia Mathematica, Tome 231 (2015), p. 265-279 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, we introduce and study the notion of completely bounded $Λ_{p}$ sets ( $Λ_{p}^{c b}$ for short) for compact, non-abelian groups G. We characterize $Λ_{p}^{c b}$ 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 $Λ_{p}^{c b}$ 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.

Publié le : 2015-01-01

Zbl 06545406

EUDML-ID : urn:eudml:doc:285615

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     author = {Kathryn Hare and Parasar Mohanty},
     title = {Completely bounded lacunary sets for compact non-abelian groups},
     journal = {Studia Mathematica},
     volume = {231},
     year = {2015},
     pages = {265-279},
     zbl = {06545406},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8391-1-2016}
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Kathryn Hare; Parasar Mohanty. Completely bounded lacunary sets for compact non-abelian groups. Studia Mathematica, Tome 231 (2015) pp. 265-279. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8391-1-2016/