Generalized Orthogonal Measures on the Space of Unital Completely Positive Maps
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912013798604800 |
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| author | Bhattacharya, Angshuman Kulkarni, Chaitanya J. |
| author_facet | Bhattacharya, Angshuman Kulkarni, Chaitanya J. |
| contents | A classical result by Effros connects the barycentric decomposition of a state on a C*-algebra to the disintegration of the GNS representation of the state with respect to an orthogonal measure on the state space of the C*-algebra. In this note, we take this approach to the space of unital completely positive maps on a C*-algebra with values in B(H), connecting the barycentric decomposition of the unital completely positive map and the dis-integration of the minimal Stinespring dilation of the same. This generalizes Effros' work in the non-commutative setting. We do this by introducing a special class of barycentric measures which we call generalized orthogonal measures. We end this note by mentioning some examples of generalized orthogonal measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_10225 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generalized Orthogonal Measures on the Space of Unital Completely Positive Maps Bhattacharya, Angshuman Kulkarni, Chaitanya J. Operator Algebras A classical result by Effros connects the barycentric decomposition of a state on a C*-algebra to the disintegration of the GNS representation of the state with respect to an orthogonal measure on the state space of the C*-algebra. In this note, we take this approach to the space of unital completely positive maps on a C*-algebra with values in B(H), connecting the barycentric decomposition of the unital completely positive map and the dis-integration of the minimal Stinespring dilation of the same. This generalizes Effros' work in the non-commutative setting. We do this by introducing a special class of barycentric measures which we call generalized orthogonal measures. We end this note by mentioning some examples of generalized orthogonal measures. |
| title | Generalized Orthogonal Measures on the Space of Unital Completely Positive Maps |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2211.10225 |