Journal of Operator Theory

Volume 39, Issue 1, Winter 1998 pp. 43-58.

A characterization of positive elementary operators

Authors: Jin-Chuan Hou
Author institution: Department of Mathematics, Shanxi Teachers University, Linfen, 041004, P.R. CHINA

Summary: A global structure theorem is obtained for positive elementary operators from ${\cal B}({\cal H})$ into ${\cal B}({\cal K})$, where ${\cal B}({\cal H})$ is the C$^*$-algebra of all (bounded linear) operators on complex Hilbert space ${\cal H}$. Several simple criteria are given which ensure a positive elementary operator to be completely positive.

Keywords: Elementary operators, matrix-algebras, positive linear maps, complete positivity

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