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

2018/01/01 by Dan-Virgil Voiculescu, Voiculescu, Dan-Virgil
Mathematics · #47A13 (Secondary) #47L20 #47L30 (Primary) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #math.FA #math.SP #msc:47A13 #msc:47L20 #msc:47L30

paper · pdf · doi:10.48550/arxiv.1801.00490

9 pages

arxiv created 2019/04/03 · arxiv updated 2019/04/04

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.

Related

• K-theory and perturbations of absolutely continuous spectra
• Lebesgue decomposition of functionals and unique preduals for commutants modulo normed ideals
• Complete wave operators in non-selfadjoint Kato model of smooth perturbation theory
• Weak type estimates for the absolute value mapping
• Commutants mod Normed Ideals