Amenable representations and finite injective von Neumann algebras
HTML articles powered by AMS MathViewer
- by Alain Valette PDF
- Proc. Amer. Math. Soc. 125 (1997), 1841-1843 Request permission
Abstract:
Let $U(M)$ be the unitary group of a finite, injective von Neumann algebra $M$. We observe that any subrepresentation of a group representation into $U(M)$ is amenable in the sense of Bekka; this yields short proofs of two known results—one by Robertson, one by Haagerup—concerning group representations into $U(M)$.References
- Mohammed E. B. Bekka, Amenable unitary representations of locally compact groups, Invent. Math. 100 (1990), no. 2, 383–401. MR 1047140, DOI 10.1007/BF01231192
- Mohammed E. B. Bekka and Alain Valette, Kazhdan’s property $(\textrm {T})$ and amenable representations, Math. Z. 212 (1993), no. 2, 293–299. MR 1202813, DOI 10.1007/BF02571659
- A. Connes, Classification of injective factors, Ann. of Math. 104 (1976), 585–609.
- Uffe Haagerup, Injectivity and decomposition of completely bounded maps, Operator algebras and their connections with topology and ergodic theory (Buşteni, 1983) Lecture Notes in Math., vol. 1132, Springer, Berlin, 1985, pp. 170–222. MR 799569, DOI 10.1007/BFb0074885
- Pierre de la Harpe, A. Guyan Robertson, and Alain Valette, On the spectrum of the sum of generators for a finitely generated group, Israel J. Math. 81 (1993), no. 1-2, 65–96. MR 1231179, DOI 10.1007/BF02761298
- Eberhard Kirchberg, Discrete groups with Kazhdan’s property $\textrm {T}$ and factorization property are residually finite, Math. Ann. 299 (1994), no. 3, 551–563. MR 1282231, DOI 10.1007/BF01459798
- A. Guyan Robertson, Property $(\textrm {T})$ for $\textrm {II}_1$ factors and unitary representations of Kazhdan groups, Math. Ann. 296 (1993), no. 3, 547–555. MR 1225990, DOI 10.1007/BF01445119
Additional Information
- Alain Valette
- Affiliation: Institut de Mathématiques, Université de Neuchâtel, Rue Emile Argand 11, CH-2007 Neuchâtel, Switzerland
- Email: valette@maths.unine.ch
- Received by editor(s): October 6, 1995
- Received by editor(s) in revised form: December 5, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1841-1843
- MSC (1991): Primary 22D25; Secondary 46L10
- DOI: https://doi.org/10.1090/S0002-9939-97-03754-4
- MathSciNet review: 1371145