ArticleOriginal scientific text

Title

Banach spaces with a supershrinking basis

Authors 1

Affiliations

  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Abstract

We prove that a Banach space X with a supershrinking basis (a special type of shrinking basis) without c0 copies is somewhat reflexive (every infinite-dimensional subspace contains an infinite-dimensional reflexive subspace). Furthermore, applying the c0-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 c0.

Bibliography

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Pages:
29-36
Main language of publication
English
Received
1997-07-30
Accepted
1998-05-11
Published
1999
Exact and natural sciences