## 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.

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 |

### Bibliografisk note

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