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

Krzysztof Szczygielski

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arXiv · 2512.08525

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

Krzysztof Szczygielski

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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.

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Krzysztof Szczygielski. 2025-12-09. Decomposable semigroups on C*-algebras and D-divisible dynamical maps. https://arxiv.org/abs/2512.08525

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