On the λ-property and spaces of convergent sequences.
On Two Classes of Mappings on Banach Sequenee Spaces.
On uniform Kadec–Klee properties and rotundity in generalized Cesàro sequence spaces.
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...
Orlicz sequence spaces that are uniformly rotund in a weakly compact set of directions
Necessary and sufficient conditions are given for Orlicz sequence spaces equipped with the Orlicz norm to be uniformly rotund in a weakly compact set of directions, using only conditions on the generating function of the space.
Orlicz sequence spaces with a unique spreading model.