Abstract
Let A be a norm bounded solid subset of a Banach lattice E and n be any positive integer. We prove that A is an almost Dunford-Pettis set if and only if every positive weakly compact n-homogeneous polynomial from E to c0 maps A to a relatively compact set in c0. Moreover, if E is σ-Dedekind complete, we also prove that A is an almost limited set if and only if every positive n-homogeneous polynomial from E to c0 maps A to a relatively compact set in c0.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
