2023/02/01 by Kozo Ikeda, Ikeda, Kozo, Masaki Izumi +1
Mathematics · #Advanced Algebra and Geometry #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2302.00409
openalex publication_date 2023/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In his recent work, Voiculescu generalized his remarkable formula for the quasicentral modulus of a commuting n-tuple of hermitian operators with respect to the (n,1)-Lorentz ideal to the case where its spectrum is contained in a Cantor-like self-similar set in a certain class. In this note, we treat general self-similar sets satisfying the open set condition, and obtain lower and upper bounds of the quasicentral modulus. Our proof shows that Voiculescu's formula holds for a class of self-similar sets including the Sierpinski gasket and the Sierpinski carpet.