Normal states are determined by their facial distances. (English) Zbl 1480.46075
The paper gives a beautiful result to distinguish two normal states on a semi-finite von Neumann algebra. Based on the distance to faces dependent on projections and clever using of spectral theory, the authors obtain that normal states with the same facial distances are the same for semi-finite von Neumann algebras. Hence facial distance is an interesting geometric invariant for normal states.
Reviewer: Jinsong Wu (Harbin)
MSC:
| 46L10 | General theory of von Neumann algebras |
| 46L30 | States of selfadjoint operator algebras |
| 43A30 | Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. |
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