Nonstandard hulls of lattice-normed ordered vector spaces

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.