Open AccessThe Infimum Norm of Completely Positive Maps
Author(s) -
Ching Yun Suen
Publication year - 2022
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v14n1p51
Subject(s) - infimum and supremum , mathematics , combinatorics , norm (philosophy) , corollary , discrete mathematics , political science , law
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].