On relative boundedness in operator spaces

For a canonical unbounded CP-map Lambda(.) from the vector space of densely defined closed operators on a Hilbert space H, into the vector space of de nsely defined closed operators on the symmetric Fock space over H, we prove that Lambda(A) is directly Lambda(B)-relatively bounded provided A and B a re positive and A is directly B-relatively bounded, that is, \\A Psi\\ less than or equal to c\\B psi\\ on dom(B). We consider formal generators on the symmetric Fock space corresponding to this map Lambda(.) and show that they determine uniquely certain quantum dy namical semigroups.