Hilbert modules and stochastic dilation of a quantum dynamical semigroup on a von Neumann algebra

DOI10.1007/s002200050682zbMath0935.46055OpenAlexW1971896797MaRDI QIDQ1809231

Debashish Goswami, Kalayan B. Sinha

Publication date: 16 December 1999

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002200050682

zbMATH Keywords

Markov processFock filtrationquantum stochastic dilation\(*\)-homomorphismcoordinate-free quantum stochastic calculuspartial isometry-valued processright Fock moduleuniformly continuous quantum dynamical semigroupweak Markov dilation

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Noncommutative dynamical systems (46L55) Noncommutative probability and statistics (46L53) Quantum stochastic calculus (81S25) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25)

Related Items (16)

Quantum stochastic calculus with maximal operator domains. ⋮ A REMARK ON THE STRUCTURE OF SYMMETRIC QUANTUM DYNAMICAL SEMIGROUPS ON VON NEUMANN ALGEBRAS ⋮ CP-semigroups and dilations, subproduct systems and superproduct systems: the multi-parameter case and beyond ⋮ Classification of 𝐸₀–semigroups by product systems ⋮ Remarks on the decomposition of Dirichlet forms on standard forms of von Neumann algebras ⋮ Quantum random walks and vanishing of the second Hochschild cohomology ⋮ Quantum random walks and their convergence to Evans--Hudson flows ⋮ The Unitarity Conditions for the Square of White Noise ⋮ Quantum stochastic calculus associated with quadratic quantum noises ⋮ STOCHASTIC DILATION OF A QUANTUM DYNAMICAL SEMIGROUP ON A SEPARABLE UNITAL C* ALGEBRA ⋮ UNITS FOR THE TIME-ORDERED FOCK MODULE ⋮ Quantum stochastic calculus on full Fock modules ⋮ Spatial Markov semigroups admit Hudson-Parthasarathy dilations ⋮ TENSOR PRODUCT SYSTEMS OF HILBERT MODULES AND DILATIONS OF COMPLETELY POSITIVE SEMIGROUPS ⋮ Continuous unital dilations of completely positive semigroups ⋮ Couplings to classical and non-classical squeezed white noise as stationary Markov processes

This page was built for publication: Hilbert modules and stochastic dilation of a quantum dynamical semigroup on a von Neumann algebra