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 gamma _{p,w}. Next, we present a full characterization of extreme points of the unit ball in the sequence Lorentz space gamma _{1,w}. We also establish a complete description up to isometry of the dual and predual spaces of the sequence Lorentz spaces gamma _{1,w} written in terms of the Marcinkiewicz spaces. Finally, we show a fundamental application of geometric structure of gamma _{1,w} to one-complemented subspaces of gamma _{1,w}.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.