A distance between operators acting in different Hilbert spaces and operator convergence
Functional Analysis
2025-04-30 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the ``metrics'' do not fulfill all properties of a metric (e.g. some lack the triangle inequality or the definiteness), we call them ``distances'' here. To the best of our knowledge, such distances are treated for the first time here. The present article shall serve as a starting point of further research (see e.g. arXiv:2412.13165).
Cite
@article{arxiv.2504.20971,
title = {A distance between operators acting in different Hilbert spaces and operator convergence},
author = {Olaf Post and Jan Simmer},
journal= {arXiv preprint arXiv:2504.20971},
year = {2025}
}
Comments
15 pages, 1 figure; the reference list is as in the original paper and reflects the state of the art at time of publishing (2019/2020)