The decoherence-free subalgebra of a quantum Markov semigroup on B(h).

Let T be a quantum Markov semigroup on B(h) with a faithful normal invariant state $\rho$ whose generator is represented in a generalised GKSL form $\mathcal{L}(x)=-2^{-1}\sum_\ell(L_\ell^*L_\ell x -2L_\ell^* x L_\ell + x L_\ell^*L_\ell)+i[H,x]$ with possibly unbounded $H, L_\ell$.We show that the biggest von Neumann-subalgebra N(T) of B(h) where T acts as a semigroup of automorphisms coincides with the generalised commutator of $e^{−itH}L_\ell e^{itH}$, $e^{−itH}L_\ell e^{itH}$, $t\ge 0$ under some natural regularity conditions. The proof we present here does not involve dilations T .