Operator biflatness of the Fourier algebra and approximate indicators for subgroups

Journal of Functional Analysis

Volumn 209, Issue 2, 2004, Pages 367-387

  Aristov, Oleg Yu ^a   Runde, Volker ^b   Spronk, Nico ^c  

^a Obninsk State Technical University for Nuclear Power Engineering   (Russian Federation)

^b UNIVERSITY OF ALBERTA   (Canada)

^c TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Approximately indicator; Biflatness; Fourier algebra (quantized) Banach homology; Kazhdan's property (T); Locally compact groups

Indexed keywords

EID: 1842784069     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(03)00169-1     Document Type: Article

References (36)

1. O.Yu. Aristov, Biprojective algebras and operator spaces, J. Math. Sci. (New York) 111 (2002) 3339-3386.
2. M.E.B. Bekka, Amenable unitary representations of locally compact groups, Invent. Math. 100 (1990) 383-401.
3. M.E.B. Bekka, A.T.-M. Lau, G. Schlichting, On invariant subalgebras of the Fourier-Stieltjes algebra of a locally compact groups, Math. Ann. 294 (1992) 513-522.
4. M.E.B. Bekka, P. de la Harpe, A. Valette, Property (T), Book manuscript, in preparation.
5. M.E.B. Bekka, E. Kaniuth, A.T.-M. Lau, G. Schlichting, On C*-algebras associated with locally compact groups, Proc. Amer. Math. Soc. 124 (1996) 3151-3258.
6. M.E.B. Bekka, A. Valette, On the duals of Lie groups made discrete, J. Reine Angew. Math. 439 (1993) 1-10.
7. N. Bourbaki, Intégration, Hermann, Paris, 1963.
8. J. Dixmier, Sur les représentations unitaires des groupes de Lie algébriques, Ann. Inst. Fourier (Grenoble) 7 (1957) 315-328.
9. E.G. Effros, Z.-J. Ruan, Operator Spaces, Oxford University Press, Oxford, 2000.
10. P. Eymard, L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964) 181-236.
11. J.M.G. Fell, Weak containment and induced representations of groups, II, Trans. Amer. Math. Soc. 110 (1964) 424-447.
12. E.E. Granirer, M. Leinert, On some topologies which coincide on the unit sphere of the Fourier-Stieltjes algebra B(G) and of the measure algebra M(G), Rocky Mountain J. Math. 11 (1981) 459-472.
13. P. de la Harpe, A. Valette, La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 175 (1989).
14. A. Ya. Helemskiǐ, Flat Banach modules and amenable algebras, Trans. Moscow Math. Soc. 47 (1985) 199-224 (translated from the Russian).
15. A. Ya. Helemskiǐ, The Homology of Banach and Topological Algebras, Kluwer Academic Publishers, Dordrecht, 1989 (translated from the Russian).
16. C.S. Herz, Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble) 23 (1973) 91-123.
17. E. Hewitt, K.A. Ross, Abstract Harmonical Analysis, Springer, New York, 1963.
18. B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).
19. B.E. Johnson, Approximate diagonals and cohomology of certain annihilator Banach algebras, Amer. J. Math. 94 (1972) 685-698.
20. B.E. Johnson, Non-amenability of the Fourier algebra of a compact group, J. London Math. Soc. 50 (2) (1994) 361-374.
21. E. Kaniuth, A.T.-M. Lau, A separation property of positive definite functions on locally compact groups and applications to Fourier algebras, J. Funct. Anal. 175 (2000) 89-110.
22. B.-R. Li, Introduction to Operator Algebras, World Scientific, Singapore, 1992.
23. V. Losert, H. Rindler, Almost invariant sets, Bull. London Math. Soc. 13 (1981) 145-148.
24. V. Losert, H. Rindler, Asymptotically central functions and invariant extensions of Dirac measure, in: H. Heyer (Ed.), Probability Measures on Groups, VII, Lecture Notes in Mathematics, Vol. 1064, Springer, Berlin, 1984, pp. 368-378.
25. A.L.T. Paterson, Amenability, American Mathematical Society, Providence, RI, 1988.
26. Z.-J. Ruan, The operator amenability of A(G), Amer. J. Math. 117 (1995) 1449-1474.
27. Z.-J. Ruan, G. Xu, Splitting properties of operator bimodules and operator amenability of Kac algebras, in: A. Gheondea, R.N. Gologan, D. Timotin (Eds.), Operator Theory, Operator Algebras and Related Topics, The Theta Foundation, Bucharest, 1997, pp. 193-216.
28. V. Runde, Amenability for dual Banach algebras, Studia Math. 148 (2001) 47-66.
29. V. Runde, Lectures on Amenability, in: Lecture Notes in Mathematics, Vol. 1774, Springer, Berlin, 2002.
30. Yu. V. Selivanov, Weak homological bidimension and its values in the class of biflat Banach algebras, Extracta Math. 11 (1996) 348-365.
31. N. Spronk, Operator weak amenability of the Fourier algebra, Proc. Amer. Math. Soc. 130 (2002) 3609-3617.
32. N. Spronk, Measurable Schur multipliers and completely bounded nrultipliers of the Fourier algebras, preprint, 2002.
33. R. Stokke, Quasi-central bounded approximate units in group algebras of locally compact groups, preprint, 2002.
34. P.J. Wood, Homological algebra in operator spaces with applications to harmonic analysis,I Ph.D. Thesis, University of Waterloo, 1999.
35. P.J. Wood, The operator biprojectivity of the Fourier algebra, Canad. J. Math. 54 (2002) 1100-1120.
36. R.J. Zimmer, Ergodic Theory and Semisimple Lie Groups, Birkhäuser, Basel, 1984.