On the transient and recurrent parts\cr of a quantum Markov semigroup
Volume 73 / 2006
Banach Center Publications 73 (2006), 415-428
MSC: 46L55, 82C10.
DOI: 10.4064/bc73-0-33
Abstract
We define the transient and recurrent parts of a quantum Markov semigroup $\cal{T}$ on a von Neumann algebra ${\cal A}$ and we show that, when ${\cal A}$ is $\sigma$-finite, we can write $\cal{T}$ as the sum of such semigroups. Moreover, if $\cal{T}$ is the countable direct sum of irreducible semigroups each with a unique faithful normal invariant state $\rho_n$, we find conditions under which any normal invariant state is a convex combination of $\rho_n$'s.
