A Johnson-Kist type representation for truncated vector lattices

TL;DR

This paper introduces a new generalization of truncations called maximal multi-truncations for vector lattices, providing a Johnson-Kist type representation as vector lattices of almost-finite extended-real continuous functions, with the spectrum characterized by prime ideals.

Contribution

It generalizes existing truncation concepts and offers a unified representation framework for vector lattices with maximal multi-truncations.

Findings

Provides a Johnson-Kist type representation for vector lattices with maximal multi-truncations.

Characterizes the spectrum as a set of prime ideals with hull-kernel topology.

Unifies various existing representations as special cases.

Abstract

We introduce the notion of (maximal) multi-truncations on a vector lattice as a generalization of the notion of truncations, an object of recent origin. We obtain a Johnson-Kist type representation of vector lattices with maximal multi-truncations as vector lattices of almost-finite extended-real continuous functions. The spectrum that allow such a representation is a particular set of prime ideals equipped with the hull-kernel topology. Various representations from the existing literature will appear as special cases of our general result.