On the Many Faces of the Quasicentral Modulus: from Perturbations of Operators to Noncommutative Condensers

The talk will be about a number-the quasicentral modulus-associated with an n-tuple of bounded Hilbert space operators and a rearrangement invariant norm. It underlies the multivariable generalizations
of the classical theorems of Weyl-von Neumann-Kuroda and Kato-Rosenblum in perturbation theory. On the other hand it provides an operator theory approach to Lebesgue measure and to certain other self-similar measures on fractals, as well as to the Kolmogorov-Sinai dynamical entropy. Recently a non-commutative analogy with condenser capacity in nonlinear potential theory is emerging.