The Pe lczyński Property for Tight Subspaces
نویسنده
چکیده
We show that if X is a tight subspace of C(K) then X has the Pe lczyński property and X is weakly sequentially complete. We apply this result to the space U of uniformly convergent Taylor series on the unit circle and using a minimal amount of Fourier theory prove that U has the Pe lczyński property and U is weakly sequentially complete. Using separate methods, we prove U and U have the Dunford-Pettis property. Some results concerning pointwise bounded approximation are proved for tight uniform algebras. We use tightness and the Pe lczyński property to make a remark about inner functions on strictly pseudoconvex domains in C n .
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