Some Results on Invariant States for Quantum Markov Semigroups

Given a quantum Markov semigroup ( T t ) t ≥ 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203910177/0082baec-0164-4123-9297-401a14f7d1e0/content/eq1600.tif"/> on the algebra ℬ ( ℌ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203910177/0082baec-0164-4123-9297-401a14f7d1e0/content/eq1601.tif"/> of all bounded operators on a Hilbert space h we discuss some tools for studying its invariant states and the asymptotic behaviour.