Dixmier averaging Theorem

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We know the standard result of Dixmier averaging Theorem for von Neumann algebras. Is Dixmier averaging Theorem still holds for $C^*$-algebras??






c-star-algebras von-neumann-algebras







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  • What is the statement of this theorem?
    – Aweygan
    Aug 31 at 12:13










  • The statement is following: let $A$ in vN algebra $M$, $mathcalu(M)$ is unitary group of $M$ , The norm closed convex hull of $uAu^*:u in mathcalu(M)$ intersects center of $M$.
    – mathlover
    Sep 1 at 5:56







  • 1




    In the second paragraph of the introduction to this paper, the authors state that in Dixmier's original paper he gives an example of a $C^*$-algebra for which the result fails.
    – Aweygan
    Sep 1 at 15:05














up vote
2
down vote

favorite












We know the standard result of Dixmier averaging Theorem for von Neumann algebras. Is Dixmier averaging Theorem still holds for $C^*$-algebras??






c-star-algebras von-neumann-algebras







share|cite|improve this question





















  • What is the statement of this theorem?
    – Aweygan
    Aug 31 at 12:13










  • The statement is following: let $A$ in vN algebra $M$, $mathcalu(M)$ is unitary group of $M$ , The norm closed convex hull of $uAu^*:u in mathcalu(M)$ intersects center of $M$.
    – mathlover
    Sep 1 at 5:56







  • 1




    In the second paragraph of the introduction to this paper, the authors state that in Dixmier's original paper he gives an example of a $C^*$-algebra for which the result fails.
    – Aweygan
    Sep 1 at 15:05












up vote
2
down vote

favorite









up vote
2
down vote

favorite











We know the standard result of Dixmier averaging Theorem for von Neumann algebras. Is Dixmier averaging Theorem still holds for $C^*$-algebras??






c-star-algebras von-neumann-algebras







share|cite|improve this question













We know the standard result of Dixmier averaging Theorem for von Neumann algebras. Is Dixmier averaging Theorem still holds for $C^*$-algebras??






c-star-algebras von-neumann-algebras




c-star-algebras von-neumann-algebras






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 31 at 7:39









mathlover

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14118











  • What is the statement of this theorem?
    – Aweygan
    Aug 31 at 12:13










  • The statement is following: let $A$ in vN algebra $M$, $mathcalu(M)$ is unitary group of $M$ , The norm closed convex hull of $uAu^*:u in mathcalu(M)$ intersects center of $M$.
    – mathlover
    Sep 1 at 5:56







  • 1




    In the second paragraph of the introduction to this paper, the authors state that in Dixmier's original paper he gives an example of a $C^*$-algebra for which the result fails.
    – Aweygan
    Sep 1 at 15:05
















  • What is the statement of this theorem?
    – Aweygan
    Aug 31 at 12:13










  • The statement is following: let $A$ in vN algebra $M$, $mathcalu(M)$ is unitary group of $M$ , The norm closed convex hull of $uAu^*:u in mathcalu(M)$ intersects center of $M$.
    – mathlover
    Sep 1 at 5:56







  • 1




    In the second paragraph of the introduction to this paper, the authors state that in Dixmier's original paper he gives an example of a $C^*$-algebra for which the result fails.
    – Aweygan
    Sep 1 at 15:05















What is the statement of this theorem?
– Aweygan
Aug 31 at 12:13




What is the statement of this theorem?
– Aweygan
Aug 31 at 12:13












The statement is following: let $A$ in vN algebra $M$, $mathcalu(M)$ is unitary group of $M$ , The norm closed convex hull of $uAu^*:u in mathcalu(M)$ intersects center of $M$.
– mathlover
Sep 1 at 5:56





The statement is following: let $A$ in vN algebra $M$, $mathcalu(M)$ is unitary group of $M$ , The norm closed convex hull of $uAu^*:u in mathcalu(M)$ intersects center of $M$.
– mathlover
Sep 1 at 5:56





1




1




In the second paragraph of the introduction to this paper, the authors state that in Dixmier's original paper he gives an example of a $C^*$-algebra for which the result fails.
– Aweygan
Sep 1 at 15:05




In the second paragraph of the introduction to this paper, the authors state that in Dixmier's original paper he gives an example of a $C^*$-algebra for which the result fails.
– Aweygan
Sep 1 at 15:05















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