Variations in noncommutative potential theory: finite energy states, potentials and multipliers

Abstract

In this work we undertake an extension of various aspects of the potential theory of Dirichlet forms from locally compact spaces to noncommutative C*-algebras with trace. In particular we introduce finite-energy states, potentials and multipliers of Dirichlet spaces. We prove several results among which the celebrated Deny's embedding theorem and the Deny's inequality, the fact that the carre' du champ of bounded potentials are finite-energy functionals and the relative supply of multipliers.

References in corpus (3)

• Spectral triples for the Sierpinski Gasket
• Integrals and Potentials of Differential 1-forms on the Sierpinski Gasket
• Almost normal operators mod Hilbert-Schmidt and the K-theory of the Banach algebras $E\Lambda (\Omega )$