Minimal Stinespring Representations of Operator Valued Multilinear Maps

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Minimal Stinespring Representations of Operator Valued Multilinear Maps. / Christensen, Erik.

I: Journal of Operator Theory, Bind 89, Nr. 2, 2023, s. 587-601.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Christensen, E 2023, 'Minimal Stinespring Representations of Operator Valued Multilinear Maps', Journal of Operator Theory, bind 89, nr. 2, s. 587-601. https://doi.org/10.7900/jot.2021sep04.2344

APA

Christensen, E. (2023). Minimal Stinespring Representations of Operator Valued Multilinear Maps. Journal of Operator Theory, 89(2), 587-601. https://doi.org/10.7900/jot.2021sep04.2344

Vancouver

Christensen E. Minimal Stinespring Representations of Operator Valued Multilinear Maps. Journal of Operator Theory. 2023;89(2):587-601. https://doi.org/10.7900/jot.2021sep04.2344

Author

Christensen, Erik. / Minimal Stinespring Representations of Operator Valued Multilinear Maps. I: Journal of Operator Theory. 2023 ; Bind 89, Nr. 2. s. 587-601.

Bibtex

@article{4c67f99c9fb9457d8981b8e675835b65,
title = "Minimal Stinespring Representations of Operator Valued Multilinear Maps",
abstract = "A completely positive linear map φ from a C*-algebra A into B(H) has a Stinespring representation as φ(a) = X*π(a)X, where π is a *- representation of A on a Hilbert space K and X is a bounded operator from H to K. Completely bounded multilinear operators on C*-algebras as well as some densely defined multilinear operators in Connes{\textquoteright} noncommutative geometry also have Stinespring representations of the form (Formula Presented) such that each ai is in a *-algebra Ai and X0,…, Xk are densely defined closed operators between the Hilbert spaces. We show that for both completely bounded maps and for the geometrical maps, a natural minimality assumption implies that two such Stinespring representations have unitarily equivalent *-representations in their decompositions.",
keywords = "C,-algebra, completely bounded, multilinear, noncommutative geometry, Stinespring representation, unitarily equivalent",
author = "Erik Christensen",
note = "Publisher Copyright: {\textcopyright} Copyright by THETA, 2023",
year = "2023",
doi = "10.7900/jot.2021sep04.2344",
language = "English",
volume = "89",
pages = "587--601",
journal = "Journal of Operator Theory",
issn = "0379-4024",
publisher = "Academia Romana Institutul de Matematica",
number = "2",

}

RIS

TY - JOUR

T1 - Minimal Stinespring Representations of Operator Valued Multilinear Maps

AU - Christensen, Erik

N1 - Publisher Copyright: © Copyright by THETA, 2023

PY - 2023

Y1 - 2023

N2 - A completely positive linear map φ from a C*-algebra A into B(H) has a Stinespring representation as φ(a) = X*π(a)X, where π is a *- representation of A on a Hilbert space K and X is a bounded operator from H to K. Completely bounded multilinear operators on C*-algebras as well as some densely defined multilinear operators in Connes’ noncommutative geometry also have Stinespring representations of the form (Formula Presented) such that each ai is in a *-algebra Ai and X0,…, Xk are densely defined closed operators between the Hilbert spaces. We show that for both completely bounded maps and for the geometrical maps, a natural minimality assumption implies that two such Stinespring representations have unitarily equivalent *-representations in their decompositions.

AB - A completely positive linear map φ from a C*-algebra A into B(H) has a Stinespring representation as φ(a) = X*π(a)X, where π is a *- representation of A on a Hilbert space K and X is a bounded operator from H to K. Completely bounded multilinear operators on C*-algebras as well as some densely defined multilinear operators in Connes’ noncommutative geometry also have Stinespring representations of the form (Formula Presented) such that each ai is in a *-algebra Ai and X0,…, Xk are densely defined closed operators between the Hilbert spaces. We show that for both completely bounded maps and for the geometrical maps, a natural minimality assumption implies that two such Stinespring representations have unitarily equivalent *-representations in their decompositions.

KW - C,-algebra

KW - completely bounded

KW - multilinear

KW - noncommutative geometry

KW - Stinespring representation

KW - unitarily equivalent

UR - http://www.scopus.com/inward/record.url?scp=85159915746&partnerID=8YFLogxK

U2 - 10.7900/jot.2021sep04.2344

DO - 10.7900/jot.2021sep04.2344

M3 - Journal article

AN - SCOPUS:85159915746

VL - 89

SP - 587

EP - 601

JO - Journal of Operator Theory

JF - Journal of Operator Theory

SN - 0379-4024

IS - 2

ER -

ID: 371918287