ArticleOriginal scientific text
Title
Banach spaces with a supershrinking basis
Authors 1
Affiliations
- 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 copies is somewhat reflexive (every infinite-dimensional subspace contains an infinite-dimensional reflexive subspace). Furthermore, applying the -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 .
Bibliography
- J. Diestel, Sequences and Series in Banach Spaces, Springer, 1984.
- N. Ghoussoub and B. Maurey,
-embeddings in Hilbert space, J. Funct. Anal. 61 (1985), 72-97. - J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Ergeb. Math. Grenzgeb. 92, Springer, 1977.
- G. López and J. F. Mena, RNP and KMP are equivalent for some Banach spaces with shrinking basis, Studia Math. 118 (1996), 11-17.
- H. Rosenthal, A subsequence principle characterizing Banach spaces containing
, Bull. Amer. Math. Soc. 30 (1994), 227-233. - H. Rosenthal, Boundedly complete weak-Cauchy sequences in Banach spaces, preprint.