Open AccessON SEPARATE ORDER CONTINUITY OF ORTHOGONALLY ADDITIVE OPERATORS
Author(s) -
I. Krasikova,
Marat Pliev,
Mikhail Popov,
O. Fotiy
Publication year - 2021
Publication title -
bukovinsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 2309-4001
DOI - 10.31861/bmj2021.01.17
Subject(s) - order (exchange) , mathematics , bounded function , operator (biology) , uniform continuity , first order , pure mathematics , third order , mathematical analysis , metric space , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene , philosophy , theology
Our main result asserts that, under some assumptions, the uniformly-to-order continuity of an order bounded orthogonally additive operator between vector lattices together with its horizontally-to-order continuity implies its order continuity (we say that a mapping f : E → F between vector lattices E and F is horizontally-to-order continuous provided f sends laterally increasing order convergent nets in E to order convergent nets in F, and f is uniformly-to-order continuous provided f sends uniformly convergent nets to order convergent nets).