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Köthe-Bochner spaces and some geometric properties related to rotundity and smoothness
Jan-David Hardtke
In 2000 Kadets et al. introduced the notions of acs, luacs and uacs spaces, which form common generalisations of well-known rotundity and smoothness properties of Banach spaces. In…
On convergence with respect to an ideal and a family of matrices
Jan-David Hardtke
Recently P. Das, S. Dutta and E. Savas introduced and studied the notions of strong -summability with respect to an Orlicz function and -statistical convergence, wher…
Some remarks on stronger versions of the Boundary Problem for Banach spaces
Jan-David Hardtke
Let be a real Banach space. A subset of the dual unit sphere of is said to be a boundary for , if every element of attains its norm on some functional in . Th…
Rainwater-Simons-type convergence theorems for generalized convergence methods
Jan-David Hardtke
We extend the well-known Rainwater-Simons convergence theorem to various generalized convergence methods such as strong matrix summability, statistical convergence and almost conve…