Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 60
Compactness properties of limited operators
Farid Afkir, Aziz Elbour
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
December 27, 2021
March 03, 2061
April 15, 2061

Abstract: This communication is devoted to study the class of limited operators on Banach lattices (that is Banach spaces with partial order), this class of operators was introduced by studied by a number of authors, in particular Bourgain [3]. This communication studied the relation between the “limited (ness)” and “weak compactness” properties. More precisely, if every limited operator from a Banach lattice $E$ into a Banach space $X$ is weakly compact (resp. compact) then the norm of dual of $E$ is order continuous or $X$ has the (DB) (resp. Gelfand –Philips) property. Also, it is proved ...