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

• URL: http://arxiv.org/abs/2306.15952v2
• Date: Mon, 27 May 2024 07:07:42 GMT
• Title: A minimal completion theorem and almost everywhere equivalence for Completely Positive maps
• Authors: B. V. Rajarama Bhat, Arghya Chongdar,
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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