Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONSTRUCTION OF UNBOUNDED DIRICHLET FOR ON STANDARD FORMS OF VON NEUMANN ALGEBRAS

  • Bahn, Chang-Soo (Institute of Natural Science, Yonsei University) ;
  • Ko, Chul-Ki (Department of Mathematics, Seoul National University)
  • Published : 2002.11.01
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Abstract

We extend the construction of Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebra given in [13] to the case of unbounded operators satiated with the von Neumann algebra. We then apply our result to give Dirichlet forms associated to the momentum and position operators on quantum mechanical systems.

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References

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  1. Remarks on the decomposition of Dirichlet forms on standard forms of von Neumann algebras vol.48, pp.11, 2007, https://doi.org/10.1063/1.2804751
  2. REMARKS ON THE STRUCTURE OF DIRICHLET FORMS ON STANDARD FORMS OF VON NEUMANN ALGEBRAS vol.08, pp.02, 2005, https://doi.org/10.1142/S0219025705001925
  3. Ergodic property of Markovian semigroups on standard forms of von Neumann algebras vol.46, pp.11, 2005, https://doi.org/10.1063/1.2113067
  4. DIRICHLET FORMS AND SYMMETRIC MARKOVIAN SEMIGROUPS ON ℤ2-GRADED VON NEUMANN ALGEBRAS vol.15, pp.08, 2003, https://doi.org/10.1142/S0129055X03001825
  5. Construction of a family of quantum Ornstein–Uhlenbeck semigroups vol.45, pp.2, 2004, https://doi.org/10.1063/1.1641150