Minimal Stinespring Representations of Operator Valued Multilinear Maps
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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.
Originalsprog | Engelsk |
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Tidsskrift | Journal of Operator Theory |
Vol/bind | 89 |
Udgave nummer | 2 |
Sider (fra-til) | 587-601 |
Antal sider | 15 |
ISSN | 0379-4024 |
DOI | |
Status | Udgivet - 2023 |
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© Copyright by THETA, 2023
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- https://www.theta.ro/jot/archive/2023-089-002/2023-089-002-009.pdf
Forlagets udgivne version
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