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Results tagged with c-star-algebras
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user 147609
A C*-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (a b)* = b* a* and the C*-identity ‖a* a‖ = ‖a‖². Related tags: [banach-algebras], [von-neumann-algebras], [operator-algebras], [spectral-theory].
5
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1
answer
407
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Faithful traces on quasi-diagonal C*-algebras
Recall that a separable C*-algebra $A$ is quasi-diagonal if there are completely positive and contractive maps $\varphi_k \colon A \rightarrow M_{n(k)}$ such that $||\varphi_k(ab) - \varphi_k(a)\varph …
- 733
2
votes
0
answers
118
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Does this groupoid have a quasi-diagonal reduced $C^*$-algebra?
Let $H$ be a discrete group, and let $X$ be the one-point compactification of $\mathbb{N}$. Consider the étale groupoid $G = H \times \{\infty\} \sqcup \mathbb{N}$, whose unit space is $X$, and with o …
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1
vote
1
answer
470
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When do completely positive maps have a closed image?
Let $\mathcal{A}, \mathcal{B}$ be C*-algebras. A map $\phi \colon \mathcal{A} \rightarrow \mathcal{B}$ is completely positive (cp) if it's linear, * preserving and all of its' coordinatewise extension …
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0
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Amenable non-Hausdorff groupoids
Just to add to my comment, the definition of amenability is the same in the Hausdorff/non-Hausdorff settings (as long as $G$ is assumed to be étale). In particular, what we want are functions $(\xi_i) …
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