The condenser quasicentral modulus

TL;DR

This paper introduces the condenser quasicentral modulus, a new concept for analyzing operator perturbations, explores its properties, computes examples, and discusses related variational problems within a broader algebraic framework.

Contribution

It defines and studies the condenser quasicentral modulus, extending the concept to semifinite von Neumann algebras and connecting it with nonlinear potential theory.

Findings

Established basic properties of the condenser quasicentral modulus

Computed a simple example illustrating the concept

Discussed variational problems related to the modulus

Abstract

We introduced the quasicentral modulus to study normed ideal perturbations of operators. It is a limit of condenser quasicentral moduli in view of a recently noticed analogy with capacity in nonlinear potential theory. We prove here some basic properties of the condenser quasicentral modulus and compute a simple example. We also discuss some associated variational problems. Part of the results are in the more general setting of a semifinite von Neumann algebra.