Y.M. Park
Construction of Dirichlet Forms and
Standard Forms of von Neumann Algebras
(558K, Postscript)
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.