Central sequences associated with a state
HTML articles powered by AMS MathViewer
- by Sze Kai Tsui PDF
- Proc. Amer. Math. Soc. 82 (1981), 76-80 Request permission
Abstract:
Central sequences associated with a state are defined and used to derive a characterization of the factor state in question. This characterization is used to study the factor state extension problem. One of the affirmative results obtained in this paper is as follows. Let $\mathcal {A}_1$, be a finite dimensional sub-${C^ * }$*-algebra of $\mathcal {A}$. Then every factor state on the relative commutant of $\mathcal {A}_1$, in $\mathcal {A}$ extends to a factor state on $\mathcal {A}$.References
-
Charles Akemann and Gert Pedersen, Central sequences and inner derivations of separable ${C^ * }$-algebras, preprint.
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars Éditeur, Paris, 1969 (French). Deuxième édition. MR 0246136
- George A. Elliott, Some $C^*$-algebras with outer derivations. III, Ann. of Math. (2) 106 (1977), no. 1, 121–143. MR 448093, DOI 10.2307/1971162
- Dusa McDuff, Central sequences and the hyperfinite factor, Proc. London Math. Soc. (3) 21 (1970), 443–461. MR 281018, DOI 10.1112/plms/s3-21.3.443
- Shôichirô Sakai, On automorphism groups of $\textrm {II}_{1}$-factors, Tohoku Math. J. (2) 26 (1974), 423–430. MR 380443, DOI 10.2748/tmj/1178241136 —, ${C^ * }$-algebras and ${W^ * }$-algebras, Springer-Verlag, Berlin and New York, 1971.
- I. E. Segal, Irreducible representations of operator algebras, Bull. Amer. Math. Soc. 53 (1947), 73–88. MR 20217, DOI 10.1090/S0002-9904-1947-08742-5 Jun Tomiyama, Tensor products and projections of norm one in von Neumann algebras, Seminar at Univ. of Copenhagen, 1970.
- Kôsaku Yosida, Functional analysis, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York, Inc., New York, 1968. MR 0239384
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 76-80
- MSC: Primary 46L30
- DOI: https://doi.org/10.1090/S0002-9939-1981-0603605-6
- MathSciNet review: 603605