Nonstandard hulls of lattice-normed ordered vector spaces

Authors

ABDULLAH AYDIN
SVETLANA GOROKHOVA
HASAN GÜL

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.

DOI

10.3906/mat-1612-59

Keywords

Vector lattice, ordered vector space, lattice-normed space, decomposable lattice norm, associated Banach--Kantorovich space, lattice-normed ordered vector space, nonstandard hull

First Page

155

Last Page

163

Recommended Citation

AYDIN, ABDULLAH; GOROKHOVA, SVETLANA; and GÜL, HASAN (2018) "Nonstandard hulls of lattice-normed ordered vector spaces," Turkish Journal of Mathematics: Vol. 42: No. 1, Article 14. https://doi.org/10.3906/mat-1612-59
Available at: https://journals.tubitak.gov.tr/math/vol42/iss1/14