Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich. mehr Informationen...
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.