The amenability constant of the Fourier algebra

Proceedings of the American Mathematical Society

Volumn 134, Issue 5, 2006, Pages 1473-1481

  Runde, Volker ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Almost abelian group; Amenability constant; Amenable Banach algebra; Completely bounded map; Fourier algebra; Locally compact group

Indexed keywords

EID: 33646736335     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-05-08164-5     Document Type: Article

References (23)

1. [Con et al.] J. H. CONWAY, Atlas of Finite Groups. Clarendon Press, 1985. MR0827219 (88g:20025)
2. [E-R] E. G. EFFROS and Z.-J. RUAN, Operator Spaces. Clarendon Press, 2000. MR1793753 (2002a:46082)
3. [E-S] M. ENOCK and J.-M. SCHWARTZ, Kac Algebras and Duality of Locally Compact Groups (with a preface by A. Connes and a postface by A. Ocneanu). Springer-Verlag, 1992. MR1215933 (94e:46001)
4. [Eym] P. EYMARD, L'algèbre de Fourier d'un groupe localement compact. Bull. Soc. Math. France 92 (1964), 181-236. MR0228628 (37:4208)
5. [For et al.] B. E. FORREST, E. KANIUTH, A. T.-M. LAU, and N. SPRONK, Ideals with bounded approximate identities in Fourier algebras. J. Funct. Anal 203 (2003), 286-304. MR1996874 (2004e:43002)
6. [F-R] B. E. FORREST and V. RUNDE, Amenability and weak amenability of the Fourier algebra. Math. Z. 250 (2005), 731-744.
7. [F-W] B. E. FORREST and P. J. WOOD, Cohomology and the operator space structure of the Fourier algebra and its second dual. Indiana Univ. Math. J. 50 (2001), 1217-1240. MR1871354 (2003d:43007)
8. [Haa] U. HAAGERUP, All nuclear C*-algebras are amenable. Invent. Math. 74 (1983), 305-319. MR0723220 (85g:46074)
9. [Hos] B. HOST, Le théorème des idempotents dans B(G). Bull. Soc. Math. France 114 (1986), 215-223. MR0860817 (88b:43003)
10. [I-S] M. ILIE and N. SPRONK, Completely bounded homomorphisms of the Fourier algebras. J. Funct. Anal. 225 (2005), 480-499. MR2152508
11. [Joh1] B. E. JOHNSON, Cohomology in Banach algebras. Mem. Amer. Math. Soc. 127 (1972). MR0374934 (51:11130)
12. [Joh2] B. E. JOHNSON, Approximate diagonals and Cohomology of certain annihilator Banach algebras. Amer. J. Math. 94 (1972), 685-698. MR0317050 (47:5598)
13. [Joh3] B. E. JOHNSON, Non-amenability of the Fourier algebra of a compact group. J. London Math. Soc. (2) 50 (1994), 361-374. MR1291743 (95i:43001)
14. [L-L-W] A. T.-M. LAU, R. J. LOY, and G. A. WILLIS, Amenability of Banach and C*-algebras on locally compact groups. Studia Math. 119 (1996), 161-178. MR1391474 (97d:46065)
15. [Lep] H. LEPTIN, Sur l'algèbre de Fourier d'un groupe localement compact. C. R. Acad. Sci. Paris, Sér. A 266 (1968), 1180-1182. MR0239002 (39:362)
16. [Los] V. LOSERT, On tensor products of Fourier algebras. Arch. Math. (Basel) 43 (1984), 370-372. MR0802314 (87c:43004)
17. [Moo] C. C. MOORE, Groups with finite dimensional irreducible representations. Trans. Amer. Math. Soc. 166 (1972), 401-410. MR0302817 (46:1960)
18. [Pie] J. P. PIER, Amenable Locally Compact Groups. Wiley-Interscience, 1984. MR0767264 (86a:43001)
19. [Rua] Z.-J. RUAN, The operator amenability of A(G). Amer. J. Math. 117 (1995), 1449-1474. MR1363075 (96m:43001)
20. [Run] V. RUNDE, Lectures on Amenability. Lecture Notes in Mathematics 1774, Springer Verlag, 2002. MR1874893 (2003h:46001)
21. [Sae] S. SAEKI, On norms of idempotent measures. Proc. Amer. Math. Soc. 19 (1968), 600-602. MR0225102 (37:697)
22. [Sto] R. STOKKE, Approximate diagonals and Følner conditions for amenable group and semigroup algebras. Studia Math. 164 (2004), 139-159. MR2079635
23. [Tho] E. THOMA, Eine Charakterisierung diskreter Gruppen vom Typ I. Invent. Math. 6 (1968), 190-196. MR0248288 (40:1540)