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.
Original language | English |
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Journal | Journal of Operator Theory |
Volume | 89 |
Issue number | 2 |
Pages (from-to) | 587-601 |
Number of pages | 15 |
ISSN | 0379-4024 |
DOIs | |
Publication status | Published - 2023 |
Bibliographical note
Publisher Copyright:
© Copyright by THETA, 2023
- C,-algebra, completely bounded, multilinear, noncommutative geometry, Stinespring representation, unitarily equivalent
Research areas
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- https://www.theta.ro/jot/archive/2023-089-002/2023-089-002-009.pdf
Final published version
ID: 371918287