Variations in noncommutative potential theory: finite energy states, potentials and multipliers
Operator Algebras
2021-06-01 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1207.3524,
title = {Variations in noncommutative potential theory: finite energy states, potentials and multipliers},
author = {Fabio Cipriani and Jean-Luc Sauvageot},
journal= {arXiv preprint arXiv:1207.3524},
year = {2021}
}