On Banach Spaces with the Gelfand-Philips Property.
On Bárány's theorems of Carathéodory and Helly type
The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads as follows:...
On Compactness in L...(..., X) in the Weak Topology and in the Topology ...(L...(..., X), L...(..., X')).
On having a countable cover by sets of small local diameter
A characterization of topological spaces admitting a countable cover by sets of small local diameter close in spirit to known characterizations of fragmentability is obtained. It is proved that if X and Y are Hausdorff compacta such that C(X) has an equivalent p-Kadec norm and has a countable cover by sets of small local norm diameter, then has a countable cover by sets of small local norm diameter as well.
On nicely smooth Banach spaces.
On operators that preserve the Radon-Nikodým property.
On -reflexive Banach spaces
A Banach space is called -reflexive if for any cover of by weakly open sets there is a finite subfamily covering some ball of radius 1 centered at a point with . We prove that an infinite-dimensional separable Banach space is -reflexive (-reflexive for some ) if and only if each -net for has an accumulation point (resp., contains a non-trivial convergent sequence) in the weak topology of . We show that the quasireflexive James space is -reflexive for no . We do not know...
On some properties of hyperconvex spaces.
On spaces with local unconditional structure
On the Bishop-Phelps-Bollobás theorem for operators and numerical radius
We study the Bishop-Phelps-Bollobás property for numerical radius (for short, BPBp-nu) of operators on ℓ₁-sums and -sums of Banach spaces. More precisely, we introduce a property of Banach spaces, which we call strongly lush. We find that if X is strongly lush and X ⊕₁ Y has the weak BPBp-nu, then (X,Y) has the Bishop-Phelps-Bollobás property (BPBp). On the other hand, if Y is strongly lush and has the weak BPBp-nu, then (X,Y) has the BPBp. Examples of strongly lush spaces are C(K) spaces, L₁(μ)...
On the dual space of
On the Dunford-Pettis property
On the Dunford-Pettis property in Banach spaces
On the Gelfand-Philips Property in ?-tensor Products.
On the Gelfand-Phillips property in Banach spaces with PRI.
On the Radon-Nikodym property in locally convex spaces and the completeness of L1ε.
On the relationships between Hp(T,X/Y) and Hp(T,X)/ Hp(T,Y).
On the structure of non-dentable subsets of
It is shown that there is no closed convex bounded non-dentable subset K of such that on subsets of K the PCP and the RNP are equivalent properties. Then applying the Schachermayer-Rosenthal theorem, we conclude that every non-dentable K contains a non-dentable subset L so that on L the weak topology coincides with the norm topology. It follows from known results that the RNP and the KMP are equivalent on subsets of .
On the Surjective Dunford-Pettis Property.
On the surjective Dunford-Pettis property