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J. Korean Math. Soc. 2002; 39(6): 931-951
Printed November 1, 2002
Copyright © The Korean Mathematical Society.
Construction of unbounded Dirichlet forms on standard forms of von Neumann algebras
Changsoo Bahn
Yonsei University and Seoul National University
We extend the construction of Dirichlet forms and Mar-kovian semigroups on standard forms of von Neumann algebra given in [13] to the case of unbounded operators affiliated 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.
Keywords: Dirichlet forms, unbounded operators, Markovian semigroups, standard forms of von Neumann algebras
MSC numbers: 47D07, 46L57, 82C10
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