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(H) for
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.
Abstract We analyze semigroups of decomposable maps on CC*-algebras in context of the algebraic structure of associated infinitesimal generators. Case of von Neumann algebras, including B ( H ) for 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 and conclude with some simple examples. 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.