## 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’ noncommutative geometry also have Stinespring representations of the form (Formula Presented) such that each ai is in a *-algebra Ai and X_{0},…, X_{k} 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

## Keywords

- C,-algebra
- completely bounded
- multilinear
- noncommutative geometry
- Stinespring representation
- unitarily equivalent