The formula for the quasicentral modulus in the case of spectral measures on fractals

Abstract

We prove a general ampliation homogeneity result for the quasicentral modulus of an $n$-tuple of operators with respect to the $(p,1)$ Lorentz normed ideal. We use this to prove a formula involving Hausdorff measure for the quasicentral modulus of $n$-tuples of commuting Hermitian operators whose spectrum is contained in certain Cantor-like selfsimilar fractals.