WHAT TYPE OF DYNAMICS ARISE IN E0-DILATIONS OF COMMUTING QUANTUM MARKOV SEMIGROUPS?

DOI10.1142/S0219025708003166zbMath1167.46041arXiv0711.2876MaRDI QIDQ3548309

Orr Moshe Shalit

Publication date: 11 December 2008

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2876

zbMATH Keywords

minimal dilationCP-semigroup\(E_0\)-semigrouptwo-parameter semigroupcocycle conjugacy.

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Noncommutative dynamical systems (46L55) Noncommutative probability and statistics (46L53) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

Related Items (6)

Examples of multiparameter CCR flows with non-trivial index ⋮ On the existence of E0-semigroups — the multiparameter case ⋮ CP-semigroups and dilations, subproduct systems and superproduct systems: the multi-parameter case and beyond ⋮ Arveson's characterisation of CCR flows: the multiparameter case ⋮ Dilation theory: a guided tour ⋮ MEASURABLE -SEMIGROUPS ARE CONTINUOUS

Cites Work

• \(\text E_0\)-dilation of strongly commuting \(\text{CP}_0\)-semigroups
• INDUCTION OF SEMIGROUPS OF ENDOMORPHISMS OF ${\mathfrak B} ({\mathfrak h})$ FROM COMPLETELY POSITIVE SEMIGROUPS OF (n × n) MATRIX ALGEBRAS
• ON THE INDEX AND DILATIONS OF COMPLETELY POSITIVE SEMIGROUPS
• QUANTUM MARKOV PROCESSES (CORRESPONDENCES AND DILATIONS)
• An Index Theory For Quantum Dynamical Semigroups

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