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arXiv · 2302.00409

Quasicentral modulus and self-similar sets: a supplementary result to Voiculescu's work

Kozo Ikeda·Masaki Izumi
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Abstract

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.

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Kozo Ikeda, Masaki Izumi. 2023-02-01. Quasicentral modulus and self-similar sets: a supplementary result to Voiculescu's work. https://arxiv.org/abs/2302.00409

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