Kolmogorov's existence theorem for Markov processes in \(C^*\) algebras

DOI10.1007/BF02830889zbMath0796.60092MaRDI QIDQ1322377

B. V. Rajarama Bhat, K. R. Parthasarathy

Publication date: 20 September 1994

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

zbMATH Keywords

completely positive mapsquantum Markov processesChapman-Kolmogorov equationsGNS principleKolmogorov's existence theorem

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Markov processes (60J99)

Related Items (10)

Markov shift in non-commutative probability. ⋮ Poisson boundaries of II₁ factors ⋮ On the set of Gibbs measures for model with a countable set of spin values on Cayley trees ⋮ Quantum stochastic calculus and quantum Gaussian processes ⋮ Jones index of a quantum dynamical semigroup ⋮ Representations of homogeneous quantum Levy fields ⋮ Weak Markov processes as linear systems ⋮ Pure inductive limit state and Kolmogorov's property ⋮ CONSTRUCTING EXTENSIONS OF CP-MAPS VIA TENSOR DILATIONS WITH THE HELP OF VON NEUMANN MODULES ⋮ Introduction to Classical and Quantum Markov Semigroups

Cites Work

• Unnamed Item
• Markov quantum semigroups admit covariant Markov \(C^ *\)-dilations
• Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory
• Dilation of a Dissipative Quantum Dynamical System to a Quantum Markov Process
• Quantum stochastic processes

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