On the Birman-Krein Theorem
Mathematical Physics
2022-10-17 v1 Functional Analysis
math.MP
Abstract
It is shown that if is a unitary operator so that a singular subspace of~ is unitarily equivalent to a singular subspace of~ (or ), for each unitary operator~, then is the identity operator. In other words, there is no nontrivial generalization of Birman-Krein Theorem that includes the preservation of a singular spectral subspace in this context.
Cite
@article{arxiv.2210.07325,
title = {On the Birman-Krein Theorem},
author = {Vanderléa R. Bazao and César R. de Oliveira and Pablo A. Diaz},
journal= {arXiv preprint arXiv:2210.07325},
year = {2022}
}