Turkish Journal of Mathematics
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).
DOI
10.55730/1300-0098.3425
Keywords
Vector lattice, orthogonally additive band operator, orthogonally additive inverse band operator, orthogonally additive disjointness preserving operator
First Page
1258
Last Page
1266
Recommended Citation
TURAN, BAHRİ and TÜLÜ, DEMET
(2023)
"On orthogonally additive band operators and orthogonally additive disjointness preserving operators,"
Turkish Journal of Mathematics: Vol. 47:
No.
4, Article 15.
https://doi.org/10.55730/1300-0098.3425
Available at:
https://journals.tubitak.gov.tr/math/vol47/iss4/15
