A minimal completion theorem and almost everywhere equivalence for completely positive maps

Bhat, B.; Chongdar, Arghya

doi:10.1090/proc/16921

A minimal completion theorem and almost everywhere equivalence for completely positive maps
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by B. V. Rajarama Bhat and Arghya Chongdar;

Proc. Amer. Math. Soc. 152 (2024), 4703-4715

DOI: https://doi.org/10.1090/proc/16921

Published electronically: September 10, 2024

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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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