Capacity and the quasicentral modulus

2021/07/26 by Dan-Virgil Voiculescu, Voiculescu, Dan-Virgil
Mathematics · #47L20 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Primary: 46L89 #Secondary: 31C45 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2107.11924

openalex publication_date 2021/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We point out that the quasicentral modulus is a noncommutative analogue of a nonlinear rearrangement invariant Sobolev condenser capacity. In the case of the shifts by the generators of a finitely generated group, the quasicentral modulus coincides with a corresponding nonlinear condenser capacity on the Cayley graph of the group. Some other capacities related to the quasicentral modulus are also discussed.

Related

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