Nonstandard hulls of lattice-normed ordered vector spaces

Aydin A., Gorokhova S., Gul H.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.1, pp.155-163, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1612-59
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.155-163
  • Keywords: Vector lattice, ordered vector space, lattice-normed space, decomposable lattice norm, associated Banach-Kantorovich space, lattice-normed ordered vector space, nonstandard hull
  • Middle East Technical University Affiliated: Yes

Abstract

Nonstandard hulls of a vector lattice were introduced and studied in many papers. Recently, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space due to Emelyanov, we describe and investigate the nonstandard hull of a lattice-normed space, which is the foregoing generalization of Luxemburg's nonstandard hull of a normed space.