Decomposable semigroups on C*-algebras and D-divisible dynamical maps
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912755630473216 |
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| author | Szczygielski, Krzysztof |
| author_facet | Szczygielski, Krzysztof |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_08525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decomposable semigroups on C*-algebras and D-divisible dynamical maps Szczygielski, Krzysztof Operator Algebras Mathematical Physics 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. |
| title | Decomposable semigroups on C*-algebras and D-divisible dynamical maps |
| topic | Operator Algebras Mathematical Physics |
| url | https://arxiv.org/abs/2512.08525 |