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Distinctness of spaces of Lorentz-Zygmund multipliers

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Hare K., Mohanty P.

Studia Mathematica

2005

tom 169

nr 2

143-161

We study the spaces of Lorentz-Zygmund multipliers on compact abelian groups and show that many of these spaces are distinct. This generalizes earlier work on the non-equality of spaces of Lorentz multipliers.

Completely bounded lacunary sets for compact non-abelian groups

100%

Hare K., Mohanty P.

Studia Mathematica

2015

tom 230

nr 3

265-279

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.

Ograniczanie wyników

2 Studia Mathematica

2 Hare K.

2 Mohanty P.

1 2015

1 2005

Wyniki wyszukiwania

Distinctness of spaces of Lorentz-Zygmund multipliers

Completely bounded lacunary sets for compact non-abelian groups