On irreducibility and positivity improvement of norm continuous quantum Markov semigroups
Skander Hachicha, Ikbel Nasraoui · Infinite Dimensional Analysis Quantum Probability and Related Topics · 2024
We show that for a norm continuous quantum Markov semigroup irreducibility and positivity improvement for any time [Formula: see text] are equivalent under some general conditions that hold, in particular, in the finite-dimensional case. This result is applied to quantum Markov semigroups of weak coupling limit type. We also discuss the discrete-time case.