Decomposable semigroups on C*-algebras and D-divisible dynamical maps

TL;DR

This paper investigates the structure of semigroups of decomposable maps on C*-algebras and von Neumann algebras, extending previous results on dynamical maps and generalizing Lindblad's work on completely positive semigroups.

Contribution

It provides a detailed analysis of decomposable semigroups and D-divisible dynamical maps, extending earlier results and offering a partial generalization of Lindblad's foundational work.

Findings

Extended analysis to von Neumann algebras including B(H)

Generalized results on decomposable dynamical maps on matrix algebras

Provided a partial generalization of Lindblad's theorem on semigroups

Abstract

We analyze semigroups of decomposable maps on C*-algebras in context of the algebraic structure of associated infinitesimal generators. Case of von Neumann algebras, including $B(\mathcal{H})$ for $\mathcal{H}$ a Hilbert space, is also addressed. We then elaborate on D-divisible (decomposably divisible) dynamical maps on the Banach space of trace class operators. Our analysis extends earlier results on decomposable dynamical maps on matrix algebras (J. Phys. A: Math. Theor. 56 485202) and provides a partial generalization of the seminal work of Lindblad (Commun. Math. Phys. 48 119-130) on completely positive semigroups.