Weak-star point of continuity property and Schauder bases

Ginés López Pérez; José A. Soler Arias

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arXiv · 1309.3862

Weak-star point of continuity property and Schauder bases

Ginés López Pérez·José A. Soler Arias

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Abstract

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 get that a dual space satisfies the Radon-Nikodym property if, and only if, every seminormalized topologically weak-star null tree has a boundedly complete branch, which improves some results in \cite{DF} obtained for the separable case. Also, as a consequence of the above characterization, the following result obtained in \cite{R1} is deduced: {\it every seminormalized basic sequence in a Banach space with the point of continuity property has a boundedly complete subsequence

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Ginés López Pérez, José A. Soler Arias. 2013-09-16. Weak-star point of continuity property and Schauder bases. https://arxiv.org/abs/1309.3862

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