Nuclear $C^ *$-algebras have amenable unitary groups
HTML articles powered by AMS MathViewer
- by Alan L. T. Paterson PDF
- Proc. Amer. Math. Soc. 114 (1992), 719-721 Request permission
Abstract:
Let $A$ be a unital ${C^*}$-algebra with unitary group $G$. Give $G$ the relative (Banach space) weak topology. Then $G$ is a topological group, and we show that $A$ is nuclear if and only if there exists a left invariant mean on the space of right uniformly continuous, bounded, complex-valued functions on $G$.References
-
N. Bourbaki, General topology, Addison-Wesley, Reading, MA, 1966.
- George A. Elliott, On approximately finite-dimensional von Neumann algebras. II, Canad. Math. Bull. 21 (1978), no. 4, 415â418. MR 523582, DOI 10.4153/CMB-1978-073-1
- U. Haagerup, All nuclear $C^{\ast }$-algebras are amenable, Invent. Math. 74 (1983), no. 2, 305â319. MR 723220, DOI 10.1007/BF01394319
- P. de la Harpe, MoyennabilitĂ© du groupe unitaire et propriĂ©tĂ© $P$ de Schwartz des algĂšbres de von Neumann, AlgĂšbres dâopĂ©rateurs (SĂ©m., Les Plans-sur-Bex, 1978) Lecture Notes in Math., vol. 725, Springer, Berlin, 1979, pp. 220â227 (French). MR 548116
- Alan L. T. Paterson, Amenability, Mathematical Surveys and Monographs, vol. 29, American Mathematical Society, Providence, RI, 1988. MR 961261, DOI 10.1090/surv/029
- Gert K. Pedersen, $C^{\ast }$-algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979. MR 548006
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 719-721
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1992-1076577-8
- MathSciNet review: 1076577