On the transient and recurrent parts\cr of a quantum Markov semigroup

Tom 73 / 2006

Veronica Umanità Banach Center Publications 73 (2006), 415-428 MSC: 46L55, 82C10. DOI: 10.4064/bc73-0-33


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.


  • Veronica UmanitàDipartimento di Matematica “F. Brioschi”
    Politecnico di Milano
    Piazza Leonardo da Vinci 32
    I-20133, Milano, Italy

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