A Simple Singular Quantum Markov Semigroup
We construct a quantum Markov semigroup on the von Neumann algebra B(L 2(ℝ+;ℂ)) of all bounded operators on a Hilbert space L 2(ℝ+;ℂ) with the following property: the biggest *-subalgebra of B(L 2(ℝ+;ℂ)) contained in the domain of the infinitesimal generator is not σ-weakly dense. Our semigroup is an extension of a classical Markov semigroup on L ∞(ℝ+;ℂ) with the same property.
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