Details

Autor(en) / Beteiligte

• Ikeda, Kozo
• Izumi, Masaki

Titel

Quasicentral Modulus and Self-similar Sets: A Supplementary Result to Voiculescu’s Work

Ist Teil von

• Integral equations and operator theory, 2023-06, Vol.95 (2), Article 13

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.