Displaying similar documents to “Basic sequences and reflexivity of Banach spaces”

Banach spaces with a supershrinking basis

Ginés López (1999)

Studia Mathematica

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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 .