On the domain of the effective non-Hermitian Hamiltonian in quantum markovian dynamics

arXiv:2611.15322v1 Announce Type: new Abstract: The GKLS representation of the unbounded generator of a quantum Markov semigroup crucially depends on an unbounded operator $G$, generating a strongly continuous contraction semigroup on the underlying Hilbert space, which is formally the sum of a negative self-adjoint operator $G_0$ and $-\mathrm{i}H$ with $H$ symmetric. In many situations it is useful to know the relationships between the domains of the three operators, in particular whether $\Dom(G)=\Dom(G_0)\cap\Dom(H)$ when both $G_0$ and $H$ are unbounded.