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On Lorentz-Zygmund spaces

Colin Bennett; Karl Rudnick — 1980

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 $Λ (α, p; 𝒜)$ , $α \neq [α]$ . 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...

Homogeneous algebras on the circle. I. Ideals of analytic functions

Colin Bennett; John E. Gilbert — 1972

Annales de l'institut Fourier

Let $𝒜$ be a homogeneous algebra on the circle and $𝒜^{+}$ the closed subalgebra of $𝒜$ of functions having analytic extensions into the unit disk $D$ . This paper considers the structure of closed ideals of $𝒜^{+}$ under suitable restrictions on the synthesis properties of $𝒜$ . In particular, completely characterized are the closed ideals in $𝒜^{+}$ whose zero sets meet the circle in a countable set of points. These results contain some previous results of Kahane and Taylor-Williams obtained independently.

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On Lorentz-Zygmund spaces

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

Homogeneous algebras on the circle. I. Ideals of analytic functions