Charakterizations of the Generators of Positive Semigroups on C*- and von Neumann Algebras

TL;DR

This paper extends the characterization of generators of positive semigroups from C*-algebras to von Neumann algebras, providing new insights under unitality and contractivity assumptions.

Contribution

It generalizes a known characterization from C_0-semigroups to the setting of C_0^*-semigroups on von Neumann algebras, including dual and predual cases.

Findings

Proves the Bratteli-Robinson characterization in the C_0^*-case.

Provides additional generator characterizations under unitality and contractivity.

Restates results for dual and predual semigroups.

Abstract

Generators of positive C_0-semigroups on C^*-algebras and C_0^*-semigroups on von Neumann algebras are examined. A characterization due to Bratteli and Robinson in the C_0-case is proven in the C_0^*-case. Under the additional assumptions of unitality and contractivity of the semigroup another characterization of the generator is given. This result is restated for the dual and predual semigroup.