The PelŁczyński property for tight subspaces

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Abstract

We show that ifXis a tight subspace ofC(K) thenXhas the PelŁczyński property andX* is weakly sequentially complete. We apply this result to the spaceUof uniformly convergent Taylor series on the unit circle and using a minimal amount of Fourier theory prove thatUhas the PelŁczyński property andU* is weakly sequentially complete. Using separate methods, we proveUandU* have the Dunford-Pettis property. Some results concerning pointwise bounded approximation are proved for tight uniform algebras. We use tightness and the PelŁczyński property to make a remark about inner functions on strictly pseudoconvex domains in Cn.

Original languageEnglish
Pages (from-to)86-116
Number of pages31
JournalJournal of Functional Analysis
Volume148
Issue number1
DOIs
StatePublished - Aug 1 1997

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