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Weak-star point of continuity property and Schauder bases

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López-Pérez G., Soler-Arias J.

Studia Mathematica

2013

tom 219

nr 3

225-236

We characterize the weak-star point of continuity property for subspaces of dual spaces with separable predual and we deduce that the weak-star point of continuity property is determined by subspaces with a Schauder basis in the natural setting of dual spaces of separable Banach spaces. As a consequence of the above characterization we show that a dual space has the Radon-Nikodym property if, and only if, every seminormalized topologically weak-star null tree has a boundedly complete branch, which improves some results of Dutta and Fonf (2008) obtained for the separable case. Also, as a consequence of the above characterization, the following result of Rosenthal (2007) is deduced: every seminormalized basic sequence in a Banach space with the point of continuity property has a boundedly complete subsequence.

Ograniczanie wyników

1 Studia Mathematica

1 López-Pérez G.

1 Soler-Arias J.

1 2013

Wyniki wyszukiwania

Weak-star point of continuity property and Schauder bases