On the relationships between Hp(T,X/Y) and Hp(T,X)/ Hp(T,Y).
On the smoothness of Orlicz sequence spaces equipped with Orlicz norm.
We give a criterion of smoothness of Orlicz sequence spaces with Orlicz norm.
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 Structure of Non-Weakly Compact Operators on Banach Lattices.
On the structure of the set of higher order spreading models
We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if is uncountable, then it contains an antichain of size...
On the three-space property: non-containment of lp, 1 ≤ p < ∞, or c0 subspaces.
The main result in this paper is the following: Let E be a Fréchet space having a normable subspace X isomorphic to lp, 1 ≤ p < ∞, or to c0. Let F be a closed subspace of E. Then either F or E/F has a subspace isomorphic to X.
On the λ-property and spaces of convergent sequences.
On two classes of Banach spaces with uniform normal structure
On uncountable unconditional bases in Banach spaces
On uniformly nonsquare points and nonsquare points of Orlicz spaces
For Orlicz spaces endowed with the Orlicz norm and the Luxemburg norm, the criteria for uniformly nonsquare points and nonsquare points are given.
On Universal separable reflexive stable spaces
On weighted James' spaces.
In this note we study the topological structure of weighted James spaces J(h). In particular we prove that J(h) is isomorphic to J if and only if the weight h is bounded. We also provide a description of J(h) if the weight is a non-decreasing sequence.
On -Chebyshev subspaces of Banach spaces.
On -porous sets in abstract spaces.
Operator and function spaces which are K-analytic
Opial's property and James' quasi-reflexive spaces
Two of James’ three quasi-reflexive spaces, as well as the James Tree, have the uniform -Opial property.
Order convexity and concavity of Lorentz spaces , 0 < p < ∞
We study order convexity and concavity of quasi-Banach Lorentz spaces , where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that contains an order isomorphic copy of . We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for . We conclude with a characterization of the type and cotype of in the case when is a normable space.
Ordinal indices and Ramsey dichotomies measuring c₀-content and semibounded completeness
We study the c₀-content of a seminormalized basic sequence (χₙ) in a Banach space, by the use of ordinal indices (taking values up to ω₁) that determine dichotomies at every ordinal stage, based on the Ramsey-type principle for every countable ordinal, obtained earlier by the author. We introduce two such indices, the c₀-index and the semibounded completeness index , and we examine their relationship. The countable ordinal values that these indices can take are always of the form . These results...
Ordinal indices in Banach spaces.
Orlicz and unconditionally convergent series in L¹
We revisit Orlicz's proof of the square summability of the norms of the terms of an unconditionally convergent series in L¹. The result is then used to motivate abstract generalizations and concrete improvements.