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Mathematics > Operator Algebras

arXiv:1812.08123 (math)
[Submitted on 19 Dec 2018 (v1), last revised 5 Nov 2019 (this version, v2)]

Title:Roots of Completely Positive Maps

Authors:B.V. Rajarama Bhat, Robin Hillier, Nirupama Mallick, Vijaya Kumar U
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Abstract:We introduce the concept of completely positive roots of completely positive maps on operator algebras. We do this in different forms: as asymptotic roots, proper discrete roots and as continuous one-parameter semigroups of roots. We present structural and general existence and non-existence results, some special examples in settings where we understand the situation better, and several challenging open problems. Our study is closely related to Elfving's embedding problem in classical probability and the divisibility problem of quantum channels.
Comments: 16 pages, v2: minor corrections, added references, to appear in Lin. Alg. Appl
Subjects: Operator Algebras (math.OA); Probability (math.PR); Quantum Physics (quant-ph)
MSC classes: 46L57, 81P45
Cite as: arXiv:1812.08123 [math.OA]
  (or arXiv:1812.08123v2 [math.OA] for this version)
  https://doi.org/10.48550/arXiv.1812.08123
Journal reference: Linear Algebra and its Applications Volume 587, 15 February 2020, Pages 143-165
Related DOI: https://doi.org/10.1016/j.laa.2019.10.027

Submission history

From: Robin Hillier [view email]
[v1] Wed, 19 Dec 2018 18:07:23 UTC (20 KB)
[v2] Tue, 5 Nov 2019 15:14:37 UTC (20 KB)
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