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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.
Veronica Umanità. "On the transient and recurrent parts of a quantum Markov semigroup." Banach Center Publications 73.1 (2006): 415-428. <http://eudml.org/doc/282227>.
@article{VeronicaUmanità2006, abstract = {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.}, author = {Veronica Umanità}, journal = {Banach Center Publications}, language = {eng}, number = {1}, pages = {415-428}, title = {On the transient and recurrent parts of a quantum Markov semigroup}, url = {http://eudml.org/doc/282227}, volume = {73}, year = {2006}, }
TY - JOUR AU - Veronica Umanità TI - On the transient and recurrent parts of a quantum Markov semigroup JO - Banach Center Publications PY - 2006 VL - 73 IS - 1 SP - 415 EP - 428 AB - 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. LA - eng UR - http://eudml.org/doc/282227 ER -