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Complex Unconditional Metric Approximation Property for C Λ ( ) spaces

Daniel Li — 1996

Studia Mathematica

We study the Complex Unconditional Metric Approximation Property for translation invariant spaces C Λ ( ) 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 ( ) has (ℂ-UMAP); though these sets are such that L Λ ( ) contains functions which are not continuous, we show that there is a linear invariant lifting from these L Λ ( ) spaces into the Baire class 1 functions.

Some remarks on quasi-Cohen sets

Pascal LefèvreDaniel Li — 2001

Colloquium Mathematicae

We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets E of the dual of an abelian compact group G such that the canonical injection C ( G ) / C E c ( G ) L ² E ( G ) is a 2-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of L¹ which are isomorphic to subspaces of L¹.

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