Hybrid normed ideal perturbations of n-tuples of operators II: weak wave operators

TL;DR

This paper establishes a general weak existence theorem for wave operators under hybrid normed ideal perturbations and demonstrates the invariance of Lebesgue absolutely continuous parts of commuting hermitian operators under such perturbations.

Contribution

It introduces a new weak existence theorem for wave operators in the context of hybrid normed ideal perturbations and proves invariance results for spectral parts of operators.

Findings

Proved a general weak existence theorem for wave operators.

Showed invariance of Lebesgue absolutely continuous parts under perturbations.

Extended previous results to a broader class of hybrid normed ideal perturbations.

Abstract

We prove a general weak existence theorem for wave operators for hybrid normed ideal perturbations. We then use this result to prove the invariance of Lebesgue absolutely continuous parts of n-tuples of commuting hermitian operators under hybrid normed ideal perturbations from a class studied in the first paper of this series.