Displaying similar documents to “Some more recent results concerning weak Asplund spaces.”

Compactness in the First Baire Class and Baire-1 Operators

Mercourakis, S., Stamati, E. (2002)

Serdica Mathematical Journal

Similarity:

For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset...

Weak Baire measurability of the balls in a Banach space

José Rodríguez (2008)

Studia Mathematica

Similarity:

Let X be a Banach space. The property (∗) “the unit ball of X belongs to Baire(X, weak)” holds whenever the unit ball of X* is weak*-separable; on the other hand, it is also known that the validity of (∗) ensures that X* is weak*-separable. In this paper we use suitable renormings of ℓ ∞ ( ℕ ) and the Johnson-Lindenstrauss spaces to show that (∗) lies strictly between the weak*-separability of X* and that of its unit ball. As an application, we provide a negative answer to a question raised...