13 papers
On the dimension of the set of minimal projections
Tomasz Kobos, Grzegorz Lewicki
Let be a finite-dimensional normed space and let be its proper linear subspace. The set of all minimal projections from to is a convex subset of the spa…
A forgotten theorem of Pełczyński: -injective spaces need not be -injective -- the case
Tomasz Kania, Grzegorz Lewicki
Isbell and Semadeni [Trans. Amer. Math. Soc. 107 (1963)] proved that every infinite-dimensional -injective Banach space contains a hyperplane that is -injective…
Some remarks on contractive and existence sets
Maciej Ciesielski, Grzegorz Lewicki
Let X be a real or complex Banach space and let F in X be a non-empty set. F is called an existence set of best coapproximation (existence set for brevity), if for any x in X, $R_F…
Admissibility of Frechet spaces
Maciej Ciesielski, Grzegorz Lewicki
The aim of this paper is to to show the admissibility of some class of Frechet spaces (see Definition 2.3). In particular, this generalizes the main results of [3]. As an applicati…
Sequence Lorentz spaces and their geometric structure
Maciej Ciesielski, Grzegorz Lewicki
This article is dedicated to geometric structure of the Lorentz and Marcinkiewicz spaces in case of the pure atomic measure. We study complete criteria for order continuity, the Fa…
ON a certain class of norms in semimodular spaces and their monotonicity properties
Maciej Ciesielski, Grzegorz Lewicki
Let X be a linear space over K, K=R or K=C and let for n>1 ρ_i be s-convex semimodular defined on X for any i\in{1,...,n-1}. Put ρ=\max_{1\leq i \leq n-1}\{ρ_i\} and X_ρ= { x \in X…