A characterization of the duals of some echelon Köthe spaces of Banach valued functions.
A conjecture about the Dunford-Pettis property
A description of Banach space-valued Orlicz hearts
Let Y be a Banach space, (Ω, Σ; μ) a probability space and φ a finite Young function. It is shown that the Y-valued Orlicz heart H φ(μ, Y) is isometrically isomorphic to the l-completed tensor product of the scalar-valued Orlicz heart Hφ(μ) and Y, in the sense of Chaney and Schaefer. As an application, a characterization is given of the equality of and in terms of the Radon-Nikodým property on Y. Convergence of norm-bounded martingales in H φ(μ, Y) is characterized in terms of the Radon-Nikodým...
A Krein-Milman set without the integral representation property
A new result of G. A. Edgar on representing points in a convex bounded subset of Banach spaces with the Radon-Nikodym property as barycentres of Radon measures
A nondentable set without the tree property
A note on Banach algebras that are not isomorphic to a group algebra.
A remark on Edgar's extremal integral representation theorem
A remark on localized weak precompactness in Banach spaces
We give a characterization of -weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.
Addendum to the paper The Projecitve Tenso Product II: The Radon-Nikodym Property.
An alternative Dunford-Pettis Property
An alternative to the Dunford-Pettis Property, called the DP1-property, is introduced. Its relationship to the Dunford-Pettis Property and other related properties is examined. It is shown that -direct sums of spaces with DP1 have DP1 if 1 ≤ p < ∞. It is also shown that for preduals of von Neumann algebras, DP1 is strictly weaker than the Dunford-Pettis Property, while for von Neumann algebras, the two properties are equivalent.
Applications of some results of infinite-dimensional topology to the topological classification of operator images [Book]
Arens Semi-Regular Banach Algebras.
Arens-regularity of algebras arising from tensor norms.
Asplund Functions and Projectional Resolutions of the Identity
*Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by the Grant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.We further develop the theory of the so called Asplund functions, recently introduced and studied by W. K. Tang. Let f be an Asplund function on a Banach space X. We prove that (i) the subspace Y := sp ∂f(X) has a projectional resolution of the identity, and that (ii) if X is weakly Lindel¨of determined, then X admits a projectional...
Asplund operators and holomorphic maps.
Asplund spaces
Asplund spaces for beginners
Banach spaces which admit a norm with the uniform Kadec-Klee property
Several results are established about Banach spaces Ӿ which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from Ӿ to the Lebesgue-Bochner space if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.
Banach-Saks property in some Banach sequence spaces
It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.