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math.FA2018
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…
math.FA2018
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…