Let and be the sets of all compact operators and all bounded linear operators, respectively, on the Hilbert space . In this article, we mainly show that if , then there exist , for , such that . However, , where and are the sets of all completely bounded maps and all completely positive maps from into , respectively.
"Decompositions of completely bounded maps into completely positive maps involving trace class operators." Ann. Funct. Anal. 10 (1) 16 - 28, February 2019. https://doi.org/10.1215/20088752-2018-0005