Nonstandard Hulls of Lattice-Normed Ordered Vector Spaces

TL;DR

This paper extends the concept of nonstandard hulls from normed spaces to lattice-normed ordered vector spaces, providing a broader framework for their analysis and applications.

Contribution

It introduces and studies the nonstandard hull of lattice-normed spaces, generalizing previous work on nonstandard hulls of normed and vector lattice spaces.

Findings

Defined the nonstandard hull of lattice-normed spaces.

Established properties and structure of these hulls.

Connected the construction to Banach-Kantorovich spaces.

Abstract

Nonstandard hulls of a vector lattice were introduced and studied in \cite{E10,E9,E7,E5,E3}. In recent paper \cite{EG}, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space \cite{E8}, we describe and investigate nonstandard hull of a lattice-normed space, which is a generalization of nonstandard hull of a normed space.