On C$^*$-extreme points
HTML articles powered by AMS MathViewer
- by Bojan Magajna
- Proc. Amer. Math. Soc. 129 (2001), 771-780
- DOI: https://doi.org/10.1090/S0002-9939-00-05715-4
- Published electronically: September 19, 2000
- PDF | Request permission
Abstract:
Each weak* compact C$^*$-convex set in a hyperfinite factor (in particular in $\mathrm {B}(\mathcal {H})$) is the weak* closure of the C$^*$-convex hull of its C$^*$-extreme points.References
- William Arveson, Subalgebras of $C^{\ast }$-algebras. II, Acta Math. 128 (1972), no. 3-4, 271–308. MR 394232, DOI 10.1007/BF02392166
- A. Connes, On hyperfinite factors of type $\textrm {III}_{0}$ and Krieger’s factors, J. Functional Analysis 18 (1975), 318–327. MR 0372635, DOI 10.1016/0022-1236(75)90019-1
- A. Connes, Classification of injective factors. Cases $II_{1},$ $II_{\infty },$ $III_{\lambda },$ $\lambda \not =1$, Ann. of Math. (2) 104 (1976), no. 1, 73–115. MR 454659, DOI 10.2307/1971057
- D. R. Farenick, Kreĭn-Mil′man-type problems for compact matricially convex sets, Linear Algebra Appl. 162/164 (1992), 325–334. Directions in matrix theory (Auburn, AL, 1990). MR 1148407, DOI 10.1016/0024-3795(92)90383-L
- D. R. Farenick, $C^*$-convexity and matricial ranges, Canad. J. Math. 44 (1992), no. 2, 280–297. MR 1162344, DOI 10.4153/CJM-1992-019-1
- D. R. Farenick and Phillip B. Morenz, $C^\ast$-extreme points of some compact $C^\ast$-convex sets, Proc. Amer. Math. Soc. 118 (1993), no. 3, 765–775. MR 1139466, DOI 10.1090/S0002-9939-1993-1139466-7
- Uffe Haagerup, Connes’ bicentralizer problem and uniqueness of the injective factor of type $\textrm {III}_1$, Acta Math. 158 (1987), no. 1-2, 95–148. MR 880070, DOI 10.1007/BF02392257
- Alan Hopenwasser, Robert L. Moore, and V. I. Paulsen, $C^{\ast }$-extreme points, Trans. Amer. Math. Soc. 266 (1981), no. 1, 291–307. MR 613797, DOI 10.1090/S0002-9947-1981-0613797-5
- Alfred Rosenblatt, Sur les points singuliers des équations différentielles, C. R. Acad. Sci. Paris 209 (1939), 10–11 (French). MR 85
- Richard I. Loebl and Vern I. Paulsen, Some remarks on $C^{\ast }$-convexity, Linear Algebra Appl. 35 (1981), 63–78. MR 599846, DOI 10.1016/0024-3795(81)90266-4
- B. Magajna, C$\,^*$-convexity and the numerical range, Canad. Math. Bull. (to appear).
- Phillip B. Morenz, The structure of $C^\ast$-convex sets, Canad. J. Math. 46 (1994), no. 5, 1007–1026. MR 1295129, DOI 10.4153/CJM-1994-058-0
- S. Minakshi Sundaram, On non-linear partial differential equations of the parabolic type, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 479–494. MR 0000088
- R. R. Smith and J. D. Ward, Matrix ranges for Hilbert space operators, Amer. J. Math. 102 (1980), no. 6, 1031–1081. MR 595006, DOI 10.2307/2374180
- Corran Webster and Soren Winkler, The Krein-Milman theorem in operator convexity, Trans. Amer. Math. Soc. 351 (1999), no. 1, 307–322. MR 1615970, DOI 10.1090/S0002-9947-99-02364-8
Bibliographic Information
- Bojan Magajna
- Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia
- Email: Bojan.Magajna@fmf.uni-lj.si
- Received by editor(s): April 22, 1998
- Received by editor(s) in revised form: May 10, 1999
- Published electronically: September 19, 2000
- Additional Notes: This research was supported in part by the Ministry for Science of Slovenia
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 771-780
- MSC (2000): Primary 47L07; Secondary 46L10
- DOI: https://doi.org/10.1090/S0002-9939-00-05715-4
- MathSciNet review: 1802000