Fourier analysis, Schur multipliers on $S^p$ and non-commutative Λ(p)-sets

Asma Harcharras

ArticleOriginal scientific text

Title

Fourier analysis, Schur multipliers on $S^{p}$ and non-commutative Λ(p)-sets

Authors ¹

Affiliations

Equipe d'Analyse, Université Paris 6, 4, Place Jussieu, Case 186, 75252 Paris Cedex 05, France

Abstract

This work deals with various questions concerning Fourier multipliers on

L^{p}

, Schur multipliers on the Schatten class

S^{p}

as well as their completely bounded versions when

L^{p}

and

S^{p}

are viewed as operator spaces. For this purpose we use subsets of ℤ enjoying the non-commutative Λ(p)-property which is a new analytic property much stronger than the classical Λ(p)-property. We start by studying the notion of non-commutative Λ(p)-sets in the general case of an arbitrary discrete group before turning to the group ℤ.

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Title

Fourier analysis, Schur multipliers on Sp and non-commutative Λ(p)-sets

Affiliations

Abstract

Bibliography

Fourier analysis, Schur multipliers on $S^{p}$ and non-commutative Λ(p)-sets