ABOUT FIXED POINTS OF QUANTUM CHANNELS

We discuss the structure of the fixed points subspace for a quantum Markov map, reviewing some old and recent results. Our discussion includes various examples that illustrate a range of different scenarios, particularly highlighting the situation when the fixed points form a Von Neumann algebra. Relations with transience and recurrence properties and with absorption problems will also be examined. All this theory is applicable to both discrete and continuous time quantum Markov semigroups.