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arXiv · 2503.23248

Perturbations of operators and non-commutative condensers, an update on the quasicentral modulus

Dan-Virgil Voiculescu
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Abstract

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.

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Dan-Virgil Voiculescu. 2025-03-29. Perturbations of operators and non-commutative condensers, an update on the quasicentral modulus. https://arxiv.org/abs/2503.23248

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