Work

Commutativity and null spaces of unbounded operators on Hilbert space

Year: 2025

Type: article

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.

Source: Communications on Pure &amp Applied Analysis

DOI: 10.3934/cpaa.2025091

Authors: Richard Kadison, Simon Levin, Zhe Liu

Institutions: University of Pennsylvania, Princeton University, Georgetown University

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Army Research Office

Award: G7452299184