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Ensembles de Sidon topologiques

Myriam Dechamps-Gondim (1972)

Annales de l'institut Fourier

On étudie les ensembles de Sidon d’un groupe abélien localement compact et métrisable Γ . Après avoir démontré des résultats sur la réunion, l’élargissement et la stabilité de ces ensembles lacunaires, on détaille le résultat fondamental de ce travail : lorsque le dual G de Γ est connexe, toute partie compacte d’intérieur non vide de G est associée à tout ensemble de Sidon de Λ . Autrement dit, étant donné un compact K d’intérieur non vide de G , toute fonction bornée à valeurs complexes définie sur...

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

Asma Harcharras (1999)

Studia Mathematica

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...

Fredholm multipliers of semisimple commutative Banach algebras.

Pietro Aiena (1991)

Extracta Mathematicae

In some recent papers ([1],[2],[3],[4]) we have investigated some general spectral properties of a multiplier defined on a commutative semi-simple Banach algebra. In this paper we expose some aspects concerning the Fredholm theory of multipliers.

Homogeneous algebras on the circle. II. Multipliers, Ditkin conditions

Colin Bennett, John E. Gilbert (1972)

Annales de l'institut Fourier

This paper considers the Lipschitz subalgebras Λ ( α , p , 𝒜 ) of a homogeneous algebra on the circle. Interpolation space theory is used to derive estimates for the multiplier norm on closed primary ideals in Λ ( α , p ; 𝒜 ) , α [ α ] . From these estimates the Ditkin and Analytic Ditkin conditions for Λ ( α , p ; 𝒜 ) follow easily. Thus the well-known theory of (regular) Banach algebras satisfying the Ditkin condition applies to Λ ( α ; , p ; 𝒜 ) as does the theory developed in part I of this series which requires the Analytic Ditkin condition.Examples are discussed...

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