Positivity https://doi.org/10.1007/s11117-018-0586-1 Positivity On the class of almost L-weakly and almost M-weakly compact operators 1 2 Khalid Bouras · Driss Lhaimer · Mohammed Moussa Received: 19 September 2017 / Accepted: 17 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In this paper, we introduce and study new concepts of almost L-weakly and almost M-weakly compact operators. Keywords L-weakly compact operator · M-weakly compact operator · Almost L-weakly compact operator · Almost M-weakly compact operator · Banach lattice Mathematics Subject Classiﬁcation Primary 46B07 · Secondary 46B42 , 47B50 1 Introduction and notation Throughout this paper X and Y will denote real Banach spaces, E and F will denote real Banach lattices. B is the closed unit ball of X and sol(A) denotes the solid hull of a subset A of a Banach lattice. We will use the term operator, between two Banach spaces, to mean a bounded linear mapping. Let recall some notions and results from  and . A nonempty bounded subset A of E is said to be L-weakly compact if lim x = 0 for every disjoint sequence B Khalid Bouras email@example.com Driss Lhaimer firstname.lastname@example.org Mohammed Moussa email@example.com Department of Mathematics, Faculty
Positivity – Springer Journals
Published: May 29, 2018
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