On relative boundedness in operator spaces

For a canonical unbounded CP-map Λ(·) from the vector space of densely defined closed operators on a Hilbert space H into the vector space of densely defined closed operators on the symmetric Fock space over H, we prove that Λ(A) is directly Λ(B)-relatively bounded provided A and B are positive and A is directly B-relatively bounded, that is, ∥AΨ∥ ≤ c∥Bψ∥ on dom(B). sider formal generators on the symmetric Fock space corresponding to this map Λ(·) and show that they determine uniquely certain quantum dynamical semigroups.