On extreme extension of positive operators
Vladikavkazskij matematičeskij žurnal, Tome 26 (2024) no. 2, pp. 47-53
Voir la notice de l'article provenant de la source Math-Net.Ru
Given vector lattices $E$, $F$ and a positive operator $S$ from a majorzing subspace $D$ of $E$ to $F$, denote by $\mathcal{E}(S)$ the collection of all positive extensions of $S$ to all of $E$. This note aims to describe the collection of extreme points of the convex set $\mathcal{E}(T\circ S)$. It is proved, in particular, that $\mathcal{E}(T\circ S)$ and $T\circ\mathcal{E}(S)$ coincide and every extreme point of $\mathcal{E}(T\circ S)$ is an extreme point of $T\circ\mathcal{E}(S)$, whenever $T:F\to G$ is a Maharam operator between Dedekind complete vector lattices. The proofs of the main results are based on the three ingredients: a characterization of extreme points of subdifferentials, abstract disintegration in Kantorovich spaces, and an intrinsic characterization of subdifferentials.
@article{VMJ_2024_26_2_a3,
author = {A. G. Kusraev},
title = {On extreme extension of positive operators},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {47--53},
publisher = {mathdoc},
volume = {26},
number = {2},
year = {2024},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VMJ_2024_26_2_a3/}
}
A. G. Kusraev. On extreme extension of positive operators. Vladikavkazskij matematičeskij žurnal, Tome 26 (2024) no. 2, pp. 47-53. http://geodesic.mathdoc.fr/item/VMJ_2024_26_2_a3/