Extreme points of unital completely positive maps invariant under partial action
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913962416668672 |
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| author | Kulkarni, Chaitanya J. Hossain, Md Amir |
| author_facet | Kulkarni, Chaitanya J. Hossain, Md Amir |
| contents | The classical Choquet theorem establishes a barycentric decomposition for elements in a compact convex subset of a locally convex topological vector space. This decomposition is achieved through a probability measure that is supported on the set of extreme points of the subset. In this work, we consider a partial action $τ$ of a group $G$ on a $C^\ast$-algebra $\mathcal{A}$. For a fixed Hilbert space $\mathcal{H}$, we consider the set of all unital completely positive maps from $\mathcal{A}$ to $\mathcal{B}(\mathcal{H})$ that are invariant under the partial action $τ$. This set forms a compact convex subset of a locally convex topological vector space. To complete the picture of the barycentric decomposition provided by the classical Choquet theorem, we characterize the set of extreme points of this set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extreme points of unital completely positive maps invariant under partial action Kulkarni, Chaitanya J. Hossain, Md Amir Operator Algebras 46A55, 46B22, 46L55, 46L08, 47L07 The classical Choquet theorem establishes a barycentric decomposition for elements in a compact convex subset of a locally convex topological vector space. This decomposition is achieved through a probability measure that is supported on the set of extreme points of the subset. In this work, we consider a partial action $τ$ of a group $G$ on a $C^\ast$-algebra $\mathcal{A}$. For a fixed Hilbert space $\mathcal{H}$, we consider the set of all unital completely positive maps from $\mathcal{A}$ to $\mathcal{B}(\mathcal{H})$ that are invariant under the partial action $τ$. This set forms a compact convex subset of a locally convex topological vector space. To complete the picture of the barycentric decomposition provided by the classical Choquet theorem, we characterize the set of extreme points of this set. |
| title | Extreme points of unital completely positive maps invariant under partial action |
| topic | Operator Algebras 46A55, 46B22, 46L55, 46L08, 47L07 |
| url | https://arxiv.org/abs/2507.20797 |