The Schröder-Bernstein property for operators on Hilbert spaces

Abstract

We establish that the complete theory of a Hilbert space equipped with a normal operator has the Schröder-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.

9 pages. Fourth version: added a remark noting we were made aware of a simpler proof of a more general theorem