CONSTRUCTION OF DIRICHLET FORMS ON STANDARD FORMS OF VON NEUMANN ALGEBRAS

DOI10.1142/S0219025700000029zbMath1037.46502OpenAlexW1985701491MaRDI QIDQ4430256

Yong Moon Park

Publication date: 2000

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

Full work available at URL: https://doi.org/10.1142/s0219025700000029

zbMATH Keywords

quantum spin systemssymmetric Markovian semigroup

Mathematics Subject Classification ID

Dirichlet forms (31C25) Noncommutative probability and statistics (46L53) Quantum stochastic calculus (81S25) Quantizations, deformations for selfadjoint operator algebras (46L65)

Related Items (13)

Quantum Fokker-Planck dynamics ⋮ Dirichlet Forms on Noncommutative Spaces ⋮ Linear and nonlinear dissipative dynamics ⋮ DIRICHLET FORMS AND SYMMETRIC MARKOVIAN SEMIGROUPS ON ℤ₂-GRADED VON NEUMANN ALGEBRAS ⋮ Dirichlet forms and symmetric Markovian semigroups on CCR algebras with respect to quasi-free states ⋮ Construction of a family of quantum Ornstein–Uhlenbeck semigroups ⋮ Derivations as square roots of Dirichlet forms ⋮ The emergence of noncommutative potential theory ⋮ Remarks on the decomposition of Dirichlet forms on standard forms of von Neumann algebras ⋮ REMARKS ON THE STRUCTURE OF DIRICHLET FORMS ON STANDARD FORMS OF VON NEUMANN ALGEBRAS ⋮ Continuity and generators of dynamical semigroups for infinite Bose systems ⋮ Operator-Valued Dirichlet Forms and Module Operator Markov Semigroups ⋮ Ergodic property of Markovian semigroups on standard forms of von Neumann algebras

Cites Work

• Conditional expectations in von Neumann algebras and a theorem of Takesaki
• Finitely correlated states on quantum spin chains
• Non-commutative symmetric Markov semigroups
• Dirichlet forms and Markov semigroups on \(C^*\)-algebras
• Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras
• Some properties of modular conjugation operator of von Neumann algebras and a non-commutative Radon-Nikodym theorem with a chain rule
• KMS-symmetric Markov semigroups
• The spectral gap for some spin chains with discrete symmetry breaking
• Non-symmetric Dirichlet forms on semifinite von Neumann algebras
• QUANTUM STOCHASTIC DYNAMICS II
• Quantum stochastic processes

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