On the structure of a cone of normal unbounded completely positive maps

The paper suggests a constructive characterization of unbounded completely positive maps introduced earlier by Chebotarev for the theory of quantum dynamical semigroups. We prove that such cones are generated by a positive self-adjoint “reference” operator ΛεB(H) as follows: for any completely positive unbounded map Ф(·)εCPn*(F) these exists a completely positive normal bounded mapR(·)εCPn(H) such that ϕ(·)=ΛR(·)Λ. The class contains mappings that are unclosable sesquilinear forms. Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 194–205, February, 1999.