Sequence Lorentz spaces and their geometric structure

2018/05/16 by Ciesielski, Maciej, Lewicki, Grzegorz · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1805.06355

Abstract

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 Fatou property, strict monotonicity and strict convexity in the sequence Lorentz spaces γ_p,w. Next, we present a full characterization of extreme points of the unit ball in the sequence Lorentz space γ_1,w. We also establish a complete description with an isometry of the dual and predual spaces of the sequence Lorentz spaces γ_1,w written in terms of the Marcinkiewicz spaces. Finally, we show a fundamental application of geometric structure of γ_1,w to one-complemented subspaces of γ_1,w.

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