A minimal completion theorem and almost everywhere equivalence for Completely Positive maps

Abstract

A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some very general conditions a completely positive map almost everywhere equivalent to a quasi-pure map is actually equal to that map.

16 pages; Minors corrections, added references [5] and [7]. Accepted for publication in the Proceedings of the AMS