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Semi-embeddings and weakly sequential completeness of the projective tensor product

Qingying Bu (2005)

Studia Mathematica

We show that if P k is a boundedly complete, unconditional Schauder decomposition of a Banach space X, then X is weakly sequentially complete whenever P k X is weakly sequentially complete for each k ∈ ℕ. Then through semi-embeddings, we give a new proof of Lewis’s result: if one of Banach spaces X and Y has an unconditional basis, then X ⊗̂ Y, the projective tensor product of X and Y, is weakly sequentially complete whenever both X and Y are weakly sequentially complete.

Separable quotients of Banach spaces.

Jorge Mújica (1997)

Revista Matemática de la Universidad Complutense de Madrid

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.

Some characterizations of Banach lattices with the Schur property.

Witold Wnuk (1989)

Revista Matemática de la Universidad Complutense de Madrid

This note contains a short proof of the equivalence of the Schur and Dunford-Pettis properties in the class of discrete KB-spaces. We also present an operator characterization of the Schur property (Theorem 2) and we notice that Banach lattices which band hereditary l1 coincide with Banach lattices having the Schur property. (This characterization is due to Popa (1977)). Moreover, the paper offers examples of Banach lattices with the positive Schur property and without the Schur property and which...

Some remarks on Radon-Nikodym compact spaces

Alexander D. Arvanitakis (2002)

Fundamenta Mathematicae

The class of quasi Radon-Nikodým compact spaces is introduced. We prove that this class is closed under countable products and continuous images. It includes the Radon-Nikodým compact spaces. Adapting Alster's proof we show that every quasi Radon-Nikodým and Corson compact space is Eberlein. This generalizes earlier results by J. Orihuela, W. Schachermayer, M. Valdivia and C. Stegall. Further the class of almost totally disconnected spaces is defined and it is shown that every quasi Radon-Nikodým...

Subspaces of the Bourgain-Delbaen space

Richard Haydon (2000)

Studia Mathematica

It is shown that every infinite-dimensional closed subspace of the Bourgain-Delbaen space X a , b has a subspace isomorphic to some ℓ p .

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