2025/03/29 by Dan-Virgil Voiculescu, Voiculescu, Dan-Virgil
Mathematics · Physics and Astronomy · #46L89 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary: 47L20 #Quantum Mechanics and Non-Hermitian Physics #Secondary: 31C45 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2503.23248
openalex publication_date 2025/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is an update on the quasicentral modulus, an invariant for an n-tuple of Hilbert space operators and a rearrangement invariant norm, that plays a key-role in sharp multivariable generalizations of the classical Weyl-von Neumann-Kuroda and Kato-Rosenblum theorems of perturbation theory. There are also connections with self-similar measures on certain fractals and to the Kolmogorov-Sinai dynamical entropy. Some open problems are also pointed out. Recently a non-commutative analogy with condenser capacity in nonlinear potential theory is emerging, that provides a new perspective on the subject.