Invariant means on a class of von Neumann algebras
HTML articles powered by AMS MathViewer
- by P. F. Renaud PDF
- Trans. Amer. Math. Soc. 170 (1972), 285-291 Request permission
Abstract:
For $G$ a locally compact group with associated von Neumann algebra $VN(G)$ we prove the existence of an invariant mean on $VN(G)$. This mean is shown to be unique if and only if $G$ is discrete.References
- Richard Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839–848. MR 45941, DOI 10.1090/S0002-9939-1951-0045941-1 C. F. Dunkl and D. E. Ramirez, Existence and nonuniqueness of invariant means on ${L^\infty }(\hat G)$ (to appear).
- Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 228628
- Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
- Isaac Namioka, Partially ordered linear topological spaces, Mem. Amer. Math. Soc. 24 (1957), 50. MR 94681
- Shôichirô Sakai, On topological properties of $W^*$-algebras, Proc. Japan Acad. 33 (1957), 439–444. MR 98992
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 170 (1972), 285-291
- MSC: Primary 22D25; Secondary 43A07
- DOI: https://doi.org/10.1090/S0002-9947-1972-0304553-0
- MathSciNet review: 0304553