Geodesic
Homogeneity of the Pure State Space of a Separable ${{C}^{*}}$ -Algebra
Canadian mathematical bulletin, Tome 46 (2003) no. 3, pp. 365-372

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DOI

We prove that the pure state space is homogeneous under the action of the automorphism group (or the subgroup of asymptotically inner automorphisms) for all the separable simple ${{C}^{*}}$ -algebras. The first result of this kind was shown by Powers for the $\text{UHF}$ algbras some 30 years ago.
DOI : 10.4153/CMB-2003-038-3
Mots-clés : 46L40, 46L30 
Kishimoto, Akitaka; Ozawa, Narutaka; Sakai, Shôichirô. Homogeneity of the Pure State Space of a Separable ${{C}^{*}}$ -Algebra. Canadian mathematical bulletin, Tome 46 (2003) no. 3, pp. 365-372. doi: 10.4153/CMB-2003-038-3
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     author = {Kishimoto, Akitaka and Ozawa, Narutaka and Sakai, Sh\^oichir\^o},
     title = {Homogeneity of the {Pure} {State} {Space} of a {Separable} ${{C}^{*}}$ {-Algebra}},
     journal = {Canadian mathematical bulletin},
     pages = {365--372},
     year = {2003},
     volume = {46},
     number = {3},
     doi = {10.4153/CMB-2003-038-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-038-3/}
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