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 language | English |
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Pages (from-to) | 86-116 |
Number of pages | 31 |
Journal | Journal of Functional Analysis |
Volume | 148 |
Issue number | 1 |
DOIs | |
State | Published - Aug 1 1997 |