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.