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

2023/06/28 by B. V. Rajarama Bhat, Bhat, B. V. Rajarama, Arghya Chongdar +1 · 1 citation
Mathematics · #46L53 #47A20 #81P16 #81P47 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Operator Algebras (math.OA) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2306.15952

openalex publication_date 2023/06/28 · openalex created_date 2023/06/30 · openalex updated_date 2026/07/28

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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• Moment kernels, nested defects, and Cuntz dilations

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