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  • RootUCP190107

    Rights statement: This is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, 587, 2020 DOI: 10.1016/j.laa.2019.10.027

    Accepted author manuscript, 367 KB, PDF document

    Embargo ends: 31/10/20

    Available under license: CC BY-NC-ND

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Roots of completely positive maps

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<mark>Journal publication date</mark>15/02/2020
<mark>Journal</mark>Linear Algebra and its Applications
Volume587
Number of pages23
Pages (from-to)143-165
Publication statusPublished
Early online date31/10/19
Original languageEnglish

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.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, 587, 2020 DOI: 10.1016/j.laa.2019.10.027