Complex Unconditional Metric Approximation Property for $C_{Λ}(\mathbb{T})$ spaces

Daniel Li

ArticleOriginal scientific text

Title

Complex Unconditional Metric Approximation Property for $C_{Λ} (T)$ spaces

Authors ^1,²

Affiliations

Equipe d'Analyse, Université Paris VI, 4 Place Jussieu, 75252 Paris Cedex 05, France
Analyse Harmonique, Université Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay, France

Abstract

We study the Complex Unconditional Metric Approximation Property for translation invariant spaces

C_{Λ} (T)

of continuous functions on the circle group. We show that although some "tiny" (Sidon) sets do not have this property, there are "big" sets Λ for which

C_{Λ} (T)

has (ℂ-UMAP); though these sets are such that

L_{Λ}^{\infty} (T)

contains functions which are not continuous, we show that there is a linear invariant lifting from these

L_{Λ}^{\infty} (T)

spaces into the Baire class 1 functions.

Keywords

ENG

Unconditional Metric Approximation Property, translation invariant spaces of continuous functions, Rosenthal set, Riesz set, linear invariant lifting

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Title

Complex Unconditional Metric Approximation Property for CΛ(T) spaces

Affiliations

Abstract

Keywords

Bibliography

Complex Unconditional Metric Approximation Property for $C_{Λ} (T)$ spaces