Orthosymmetric spaces over an Archimedean vector lattice

TL;DR

This paper introduces orthosymmetric spaces over Archimedean vector lattices, generalizing finite-dimensional Euclidean spaces, and explores properties of linear operators on these new structures.

Contribution

It presents a novel generalization of Euclidean inner spaces within the framework of Archimedean vector lattices and examines linear operators in this context.

Findings

Defined orthosymmetric spaces over Archimedean vector lattices

Extended properties of linear operators to these spaces

Provided foundational results for future research

Abstract

We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.