Mixing Douglas' and weak majorization and factorization theorems
Functional Analysis
2024-11-15 v1 Optimization and Control
Abstract
The Douglas' majorization and factorization theorem characterizes the inclusion of operator ranges in Hilbert spaces. Notably, it reinforces the well-established connections between the inclusion of kernels of operators in Hilbert spaces and the (inverse) inclusion of the closures of the ranges of their adjoints. This note aims to present a ''mixed'' version of these concepts for operators with a codomain in a product space. Additionally, an application in control theory of coupled systems of linear partial differential equations is presented.
Cite
@article{arxiv.2411.09305,
title = {Mixing Douglas' and weak majorization and factorization theorems},
author = {Pierre Lissy},
journal= {arXiv preprint arXiv:2411.09305},
year = {2024}
}