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Turkish Journal of Mathematics

DOI

10.55730/1300-0098.3425

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 ${\mu }$ is a bijective orthogonally additive band operator (resp. orthogonally additive disjointness preserving operator) from $M$ into $N$ then ${\mu }^{-1}$:$N$${\rightarrow}$$M$ is an orthogonally additive band operator (resp. orthogonally additive disjointness preserving operator).

Keywords

Vector lattice, orthogonally additive band operator, orthogonally additive inverse band operator, orthogonally additive disjointness preserving operator

First Page

1258

Last Page

1266

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