This is an announcement for the paper "Some characterizations of almost limited sets and applications" by N. Machrafi, A. Elbour, and M. Moussa.

Abstract: Recently, J.X. Chen et al. introduced and studied the class of almost limited sets in Banach lattices. In this paper we establish some characterizations of almost limited sets in Banach lattices (resp. wDP* property of Banach lattices), that generalize some results obtained by J.X. Chen et al.. Also, we introduce and study the class of the almost limited operators, which maps the closed unit bull of a Banach space to an almost limited subset of a Banach lattice. Some results about the relationship between the class of almost limited operators and that of L-weakly compact (resp. M-weakly compact, resp. compact) operators are presented.

Archive classification: math.FA

Mathematics Subject Classification: 46B42 (Primary) 46B50, 47B65 (Secondary)

Remarks: 9 pages

Submitted from: azizelbour@hotmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1312.2770

or

http://arXiv.org/abs/1312.2770