COMPLETE POSITIVITY OF ELEMENTARY OPERATORS ON VON NEUMANN ALGEBRA AND THE CALKIN ALGEBRA

摘要

We prove that if R is a von Neumann algebra with no central portions of type I_n, for n > 1, then every positive elementary operator E on R is completely positive, and obtain that if H is a separable Hilbert space and E is a positive elementary operator on the Calkin algebra ε(H) = L(H)/K(H), then E is completely positive.