On Fragments on Lattice Normed Vector Lattices

BOLAT S., ERKURŞUN ÖZCAN N., Gezer N. A.

Results in Mathematics, vol.78, no.6, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 78 Issue: 6
  • Publication Date: 2023
  • Doi Number: 10.1007/s00025-023-02017-y
  • Journal Name: Results in Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Bo-fragments, Fragments, Lattice normed vector lattices
  • Hacettepe University Affiliated: Yes

Abstract

In the present paper, we investigate (bo)-fragments in lattice normed spaces. After showing that every (bo)-fragment of a positive element is a fragment in the case of lattice normed vector lattices, we prove that the collection of all (bo)-fragments of a positive element forms an order complete Boolean algebra. Several examples and detailed discussions of various cases are presented.