Banach spaces with a supershrinking basis

• Autorzy: Ginés López
• Języki publikacji: EN

Abstrakty

EN

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 $c_0$.

Kategorie tematyczne

• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 132
• Numer: 1
• Strony: 29-36

Daty

wydano

1999

otrzymano

1997-07-30

poprawiono

1998-05-11

Twórcy

autor

Ginés López

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Bibliografia

• [1] J. Diestel, Sequences and Series in Banach Spaces, Springer, 1984.
• [2] N. Ghoussoub and B. Maurey, $G_δ$-embeddings in Hilbert space, J. Funct. Anal. 61 (1985), 72-97.
• [3] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Ergeb. Math. Grenzgeb. 92, Springer, 1977.
• [4] G. López and J. F. Mena, RNP and KMP are equivalent for some Banach spaces with shrinking basis, Studia Math. 118 (1996), 11-17.
• [5] H. Rosenthal, A subsequence principle characterizing Banach spaces containing $c_0$, Bull. Amer. Math. Soc. 30 (1994), 227-233.
• [6] H. Rosenthal, Boundedly complete weak-Cauchy sequences in Banach spaces, preprint.