We define the transient and recurrent parts of a quantum Markov semigroup 𝓣 on a von Neumann algebra 𝓐 and we show that, when 𝓐 is σ-finite, we can write 𝓣 as the sum of such semigroups. Moreover, if 𝓣 is the countable direct sum of irreducible semigroups each with a unique faithful normal invariant state ρₙ, we find conditions under which any normal invariant state is a convex combination of ρₙ's.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-33,
author = {Veronica Umanit\`a},
title = {On the transient and recurrent parts of a quantum Markov semigroup},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {415-428},
zbl = {1109.46058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-33}
}
Veronica Umanità. On the transient and recurrent parts of a quantum Markov semigroup. Banach Center Publications, Tome 72 (2006) pp. 415-428. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-33/