Abstract
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.
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Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 194–205, February, 1999.
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García, J.C. On the structure of a cone of normal unbounded completely positive maps. Math Notes 65, 159–167 (1999). https://doi.org/10.1007/BF02679812
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DOI: https://doi.org/10.1007/BF02679812