Year: 2020
Type: preprint
Abstract: We show that a free vector lattice over a real vector space $V$ can be realised canonically as a vector lattice of real-valued positively homogeneous functions on any linear subspace of its dual space that separates the points of $V$. This is used to give intuition for the known fact that the free Banach lattice over a Banach space $E$ can be realised as a Banach lattice of positively homogeneous functions on $E^\ast$. It is also applied to improve the well-known result that free vector lattices over non-empty sets can be realised as vector lattices of real-valued functions. For infinite sets, the underlying spaces for such realisations can be chosen to be smaller than the usual ones.
Source: arXiv (Cornell University)
Author: de Jeu, Marcel
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4287781088