The Infimum Norm of Completely Positive Maps

Ching Yun Suen

Journal of Mathematics Research, 2022, vol. 14, issue 1, 51

Abstract: Let A be a unital C* -algebra, let L- A→B(H) be a linear map, and let ∅- A→B(H) be a completely positive linear map. We prove the property in the following- is completely positive}=inf {||T*T+TT*||1/2- L= V*TπV which is a minimal commutant representation with isometry} . Moreover, if L=L* , then is completely positive . In the paper we also extend the result is completely positive}=inf{||T||- L=V*TπV} [3 , Corollary 3.12].

Date: 2022
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