On orthogonally additive band operators and orthogonally additive disjointness preserving operators

Abstract

: Let M and N be Archimedean vector lattices. We introduce orthogonally additive band operators and orthogonally additive inverse band operators from M to N and examine their properties. We investigate the relationship between orthogonally additive band operators and orthogonally additive disjointness preserving operators and show that under some assumptions on vector lattices M or N , these two classes are the same. By using this relation, we show that if µ is a bijective orthogonally additive band operator (resp. orthogonally additive disjointness preserving operator) from M into N then µ − 1 : N → M is an orthogonally additive band operator (resp. orthogonally additive disjointness preserving operator).