Displaying similar documents to “Unconditional bases and the Radon-Nikodym property”

Separable quotients of Banach spaces.

Jorge Mújica (1997)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.

Spaces of holomorphic mappings on Banach spaces with a Schauder basis

Jorge Mujica (1997)

Studia Mathematica

Similarity:

We show that if U is a balanced open subset of a separable Banach space with the bounded approximation property, then the space ℋ(U) of all holomorphic functions on U, with the Nachbin compact-ported topology, is always bornological.

Banach spaces with a supershrinking basis

Ginés López (1999)

Studia Mathematica

Similarity:

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 .