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Banach spaces with a supershrinking basis

Ginés López — 1999

Studia Mathematica

We prove that a Banach space X with a supershrinking basis (a special type of shrinking basis) without c 0 copies is somewhat reflexive (every infinite-dimensional subspace contains an infinite-dimensional reflexive subspace). Furthermore, applying the c 0 -theorem by Rosenthal, it is proved that X contains order-one quasireflexive subspaces if X is not reflexive. Also, we obtain a characterization of the usual basis in c 0 .

Weak-star point of continuity property and Schauder bases

Ginés López-PérezJosé A. Soler-Arias — 2013

Studia Mathematica

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...

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