A Sharp Kato-Rosenblum Type Theorem for Unbounded n-Tuples

Rhishab Bhutani; Dan Virgil Voiculescu

A Sharp Kato-Rosenblum Type Theorem for Unbounded n-Tuples

Functional Analysis 2026-06-26 v1 Spectral Theory

Authors: Rhishab Bhutani , Dan Virgil Voiculescu

Abstract

We prove a generalization for commuting $n$ -tuples of unbounded self-adjoint operators and the Lorentz $(n,1)$ ideal, $n \ge 3$ , of the Kato-Rosenblum theorem. The result is derived from earlier work for bounded operators [8]. Also, a very weak result for $n=2$ unbounded operators and other additional results are obtained.

Cite

@article{arxiv.2606.28594,
  title  = {A Sharp Kato-Rosenblum Type Theorem for Unbounded n-Tuples},
  author = {Rhishab Bhutani and Dan Virgil Voiculescu},
  journal= {arXiv preprint arXiv:2606.28594},
  year   = {2026}
}

Comments

preliminary version 9 pages