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Dirichlet Forms and Markovian Semigroups on Standard Forms of von Neumann Algebras

โœ Scribed by Fabio Cipriani

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
545 KB
Volume
147
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

We characterize w*-continuous, Markovian semigroups on a von Neumann algebra M, which are , 0 -symmetric w.r.t. a faithful, normal state , 0 in M * + , in terms of quadratic forms on the Hilbert space H of a standard form (M, H, P, J). We characterize also symmetric, strongly continuous, contraction semigroups on a real Hilbert space H which leave invariant a closed, convex set in H, in terms of a contraction property of the associated quadratic forms. We apply the results to give criteria of essential selfadjointness for quadratic form sums and to give a characterization of w*-continuous, Markovian semigroups on M, which commute with the modular automorphism group _ , 0 t .

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