01-67 Changsoo Bahn, Chul Ki Ko and Yong Moon Park

Dirichlet Forms and Symmetric Markovian Semigroups on CCR Algebras with respect to Quasi-free States (102K, latex file (PCTex file)) Feb 14, 01

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Abstract. Employing the construction method of Dirichlet forms on standard forms of von Neumann algebras developed in [Park], we construct Dirichlet forms and associated symmetric Markovian semigroups on CCR algebras with respect to quasi-free states. More precisely, let A(h_o) be the CCR algebra over a complex separable pre-Hilbert space h_o and let w be a quasi-free state on A(h_o). For any normalized admissible function f and complete orthonormal system (CONS) {g_n} in h_o, we construct a Dirichlet form and corresponding symmetric Markovian semigroup on the natural standard form associated to the GNS representation of (A(h_o), w). It turns out that the form is independent of admissible function f and CONS {g_n} chosen. By analyzing the spectrum of the generator (Dirichlet operator) of the semigroup, we show that the semigroup is ergodic and tends to the equilibrium exponentially fast

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