On orthogonally additive band operators and orthogonally additive disjointness preserving operators

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TURAN B., Tulu D.

TURKISH JOURNAL OF MATHEMATICS, vol.47, no.4, pp.1258-1266, 2023 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.55730/1300-0098.3425
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1258-1266
  • Keywords: Vector lattice, orthogonally additive band operator, orthogonally additive inverse band operator, orthogo-nally additive disjointness preserving operator
  • Open Archive Collection: AVESIS Open Access Collection
  • Gazi University Affiliated: Yes

Abstract

Let M , 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 -> M is an orthogonally additive band operator (resp. orthogonally additive disjointness preserving operator).