The Schr\"oder-Bernstein property for operators on Hilbert spaces
Logic
2025-08-18 v4 Functional Analysis
Spectral Theory
Abstract
We establish that the complete theory of a Hilbert space equipped with a normal operator has the Schr\"oder-Bernstein property. This answers a question of Argoty, Berenstein, and the first-named author. We also prove an analogous statement for unbounded self-adjoint operators.
Cite
@article{arxiv.2503.20140,
title = {The Schr\"oder-Bernstein property for operators on Hilbert spaces},
author = {Nicolás Cuervo Ovalle and Isaac Goldbring and Netanel Levi},
journal= {arXiv preprint arXiv:2503.20140},
year = {2025}
}
Comments
9 pages. Fourth version: added a remark noting we were made aware of a simpler proof of a more general theorem