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• W2800974146 abstract "Let $A$ be a unital separable simple $C^*$-algebra with tracial rank zero and let $x, , yin A$ be two normal elements. We show that $x$ is in the closure of the convex full of the unitary obit of $y$ if and only if there exists a sequence of unital completely positive linear maps $phi_n$ from $A$ to $A$ such that the sequence $phi_n(y)$ convergent to $x$ in norm and also approximately preserves the trace values. A purely measure theoretical description for normal elements in the closure of convex hull of unitary orbit of $y$ is also given. In the case that $A$ has a unique tracial state some classical results about the closure of the convex hull of the unitary orbits in von Neumann algebras are proved to be hold in $C^*$-algebras setting." @default.
• W2800974146 created "2018-05-17" @default.
• W2800974146 creator A5057463546 @default.
• W2800974146 creator A5078227996 @default.
• W2800974146 date "2018-05-09" @default.
• W2800974146 modified "2023-09-27" @default.
• W2800974146 title "Convex hulls of unitary orbits of normal elements in $C^*$-algebras with tracial rank zero" @default.
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• W2800974146 doi "https://doi.org/10.48550/arxiv.1805.03396" @default.
• W2800974146 hasPublicationYear "2018" @default.
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