Non Symmetric Dirichlet Forms on Semifinite von Neumann Algebras

TL;DR

This paper extends the theory of non symmetric Dirichlet forms to semifinite von Neumann algebras, establishing fundamental correspondences and exploring examples via derivations on Hilbert algebras.

Contribution

It generalizes non symmetric Dirichlet forms to the non abelian setting and establishes key correspondences among forms, semigroups, and resolvents.

Findings

Established natural correspondences among Dirichlet forms, semigroups, and resolvents in the non abelian setting.

Provided examples of non symmetric Dirichlet forms using derivations on Hilbert algebras.

Extended the theory to semifinite von Neumann algebras.

Abstract

The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also establishing the natural correspondences among Dirichlet forms, sub-Markovian semigroups and sub-Markovian resolvents within this context. Examples of non symmetric Dirichlet forms given by derivations on Hilbert algebras are studied.