2019/12/06 by Mehrdad Bakhshi, Bakhshi, Mehrdad, Kazem Haghnejad Azar +1
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1912.04168
openalex publication_date 2019/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let E be a sublattice of a vector lattice F. A net \ xα\α∈ A⊆ E is said to be F -order convergent to a vector x ∈ E (in symbols xα\xrightarrowFo x in E), whenever there exists a net \yβ\β∈ B in F satisfying yβ\downarrow 0 in F and for each β, there exists α0 such that \vert xα- x \vert ≤ yβ whenever α≥ α0 . In this manuscript, first we study some properties of F-order convergence nets and we extend some results to the general cases. Let E and G be sublattices of vector lattices F and H respectively. We introduce FH-order continuous operators, that is, an operator T between two vector lattices E and G is said to be FH-order continuous, if xα\xrightarrowFo 0 in E implies Txα\xrightarrowHo 0 in G. We will study some properties of this new classification of operators and its relationships with order continuous operators.