Fixed points of trace preserving completely positive maps

摘要

Let A = {A(k)}(k=1)(n) be a row contraction on a separable complex Hilbert space H and Phi(A) be the normal completely positive map associated with A. We give an equivalent condition for Phi(j)(A) (I) to converge to a projection in the strong operator topology. Furthermore, it is proved that A must be a row contraction if A is a trace preserving and commuting operator sequence. Simultaneously, the fixed points set B(H)(Phi A) of Phi(A) is characterized.