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Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's (Ap) condition.

Yurii I. Lyubarskii, Kristian Seip (1997)

Revista Matemática Iberoamericana

We describe the complete interpolating sequences for the Paley-Wiener spaces Lπp (1 < p < ∞) in terms of Muckenhoupt's (Ap) condition. For p = 2, this description coincides with those given by Pavlov [9], Nikol'skii [8] and Minkin [7] of the unconditional bases of complex exponentials in L2(-π,π). While the techniques of these authors are linked to the Hilbert space geometry of Lπ2, our method of proof is based in turning the problem into one about boundedness of the Hilbert transform...

Completely bounded lacunary sets for compact non-abelian groups

Kathryn Hare, Parasar Mohanty (2015)

Studia Mathematica

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...

Completely Continuous operators

Ioana Ghenciu, Paul Lewis (2012)

Colloquium Mathematicae

A Banach space X has the Dunford-Pettis property (DPP) provided that every weakly compact operator T from X to any Banach space Y is completely continuous (or a Dunford-Pettis operator). It is known that X has the DPP if and only if every weakly null sequence in X is a Dunford-Pettis subset of X. In this paper we give equivalent characterizations of Banach spaces X such that every weakly Cauchy sequence in X is a limited subset of X. We prove that every operator T: X → c₀ is completely continuous...

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