Factorization and dilation problems for completely positive maps on von Neumann algebras

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Factorization and dilation problems for completely positive maps on von Neumann algebras. / Haagerup, Uffe; Musat, Magdalena.

I: Communications in Mathematical Physics, Bind 303, 2011, s. 555-594.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Haagerup, U & Musat, M 2011, 'Factorization and dilation problems for completely positive maps on von Neumann algebras', Communications in Mathematical Physics, bind 303, s. 555-594. https://doi.org/10.1007/s00220-011-1216-y

APA

Haagerup, U., & Musat, M. (2011). Factorization and dilation problems for completely positive maps on von Neumann algebras. Communications in Mathematical Physics, 303, 555-594. https://doi.org/10.1007/s00220-011-1216-y

Vancouver

Haagerup U, Musat M. Factorization and dilation problems for completely positive maps on von Neumann algebras. Communications in Mathematical Physics. 2011;303:555-594. https://doi.org/10.1007/s00220-011-1216-y

Author

Haagerup, Uffe ; Musat, Magdalena. / Factorization and dilation problems for completely positive maps on von Neumann algebras. I: Communications in Mathematical Physics. 2011 ; Bind 303. s. 555-594.

Bibtex

@article{79b6d773794c4443898912528176d9e1,
title = "Factorization and dilation problems for completely positive maps on von Neumann algebras",
abstract = "We study factorization and dilation properties of Markov maps between von Neumann algebras equipped with normal faithful states, i.e., completely positive unital maps which preserve the given states and also intertwine their automorphism groups. The starting point for our investigation has been the question of existence of non-factorizable Markov maps, as formulated by C. Anantharaman-Delaroche.We provide simple examples of non-factorizable Markov maps on Mn(C) for all n ≥ 3, as well as an example of a one-parameter semigroup (T (t))t≥0 of Markov maps on M4(C) such that T (t) fails to be factorizable for all small values of t > 0. As applications, we solve in the negative anopen problem in quantum information theory concerning an asymptotic version of thequantum Birkhoff conjecture, as well as we sharpen the existing lower bound estimatefor the best constant in the noncommutative little Grothendieck inequality.",
author = "Uffe Haagerup and Magdalena Musat",
year = "2011",
doi = "10.1007/s00220-011-1216-y",
language = "English",
volume = "303",
pages = "555--594",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - Factorization and dilation problems for completely positive maps on von Neumann algebras

AU - Haagerup, Uffe

AU - Musat, Magdalena

PY - 2011

Y1 - 2011

N2 - We study factorization and dilation properties of Markov maps between von Neumann algebras equipped with normal faithful states, i.e., completely positive unital maps which preserve the given states and also intertwine their automorphism groups. The starting point for our investigation has been the question of existence of non-factorizable Markov maps, as formulated by C. Anantharaman-Delaroche.We provide simple examples of non-factorizable Markov maps on Mn(C) for all n ≥ 3, as well as an example of a one-parameter semigroup (T (t))t≥0 of Markov maps on M4(C) such that T (t) fails to be factorizable for all small values of t > 0. As applications, we solve in the negative anopen problem in quantum information theory concerning an asymptotic version of thequantum Birkhoff conjecture, as well as we sharpen the existing lower bound estimatefor the best constant in the noncommutative little Grothendieck inequality.

AB - We study factorization and dilation properties of Markov maps between von Neumann algebras equipped with normal faithful states, i.e., completely positive unital maps which preserve the given states and also intertwine their automorphism groups. The starting point for our investigation has been the question of existence of non-factorizable Markov maps, as formulated by C. Anantharaman-Delaroche.We provide simple examples of non-factorizable Markov maps on Mn(C) for all n ≥ 3, as well as an example of a one-parameter semigroup (T (t))t≥0 of Markov maps on M4(C) such that T (t) fails to be factorizable for all small values of t > 0. As applications, we solve in the negative anopen problem in quantum information theory concerning an asymptotic version of thequantum Birkhoff conjecture, as well as we sharpen the existing lower bound estimatefor the best constant in the noncommutative little Grothendieck inequality.

U2 - 10.1007/s00220-011-1216-y

DO - 10.1007/s00220-011-1216-y

M3 - Journal article

VL - 303

SP - 555

EP - 594

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -

ID: 33980586