98-772 Y.M. Park

Construction of Dirichlet Forms and Standard Forms of von Neumann Algebras (558K, Postscript) Dec 30, 98

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Abstract. For a von Neumann algebra M acting on a Hilbert space H with a cyclic and seperating vector v, we give an explicit expressin of Dirichlet forms on the natural standard form (M,H,P,J) associated the pair (M,v). For any self-adjoint analytic element x of M and an admissible function f, we construct a (bounded) Dirichlet form which generates a Markovian semigruop on H. We then apply our result to construct translation invariant Markovian semigroups for quantum spin systems with finite range interactions.

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