Commutativity and Null Spaces of Unbounded Operators on Hilbert Space
Functional Analysis
2023-12-12 v1 Operator Algebras
Abstract
Based on the success of a well-known method for solving higher order linear differential equations, a study of two of the most important mathematical features of that method, viz. the null spaces and commutativity of the product of unbounded linear operators on a Hilbert space is carried out. A principle is proved describing solutions for the product of such operators in terms of the solutions for each of the factors when the null spaces of those factors satisfy a certain geometric relation to one another. Another geometric principle equating commutativity of a closed densely defined operator and a projection to stability of the range of the projection under the closed operator is proved.
Keywords
Cite
@article{arxiv.2312.06563,
title = {Commutativity and Null Spaces of Unbounded Operators on Hilbert Space},
author = {Richard Kadison and Simon Levin and Zhe Liu},
journal= {arXiv preprint arXiv:2312.06563},
year = {2023}
}