Convolutions on compact groups and fourier algebras of coset spaces

Studia Mathematica

Volumn 196, Issue 3, 2010, Pages 223-249

  Forrest, Brian E ^a   Samei, Ebrahim ^b   Spronk, Nico ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

^b UNIVERSITY OF SASKATCHEWAN   (Canada)

Author keywords

Convolution; Coset space; Fourier algebra

Indexed keywords

EID: 77649330806     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm196-3-2     Document Type: Article

References (34)

1. W. G. Bade, P. C. Curtis, and H. G. Dales, Amenability and weak amenability for Beurling and Lipschitz algebras, Proc. London Math. Soc. (3) 55 (1987), 359-377.
2. P. C. Curtis and R. J. Loy, The structure of amenable Banach algebras, J. London Math. Soc. 40 (1989), 89-104.
3. E. G. Effros and Z.-J. Ruan, On approximation properties for operator spaces, Int. J. Math. 1 (1990), 163-187.
4. -, -, Operator Spaces, London Math. Soc. Monogr. 23, Clarendon Press, New York, 2000.
5. P. Eymard, L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181-236.
6. B. E. Forrest, Fourier analysis on coset spaces, Rocky Mountain J. Math. 28 (1998), 173-190.
7. B. E. Forrest, E. Kaniuth, A. T. Lau, and N. Spronk, Ideals with bounded approximate identities in Fourier algebras, J. Funct. Anal. 203 (2003), 286-304.
8. B. E. Forrest and V. Runde, Amenability and weak amenability of the Fourier algebra, Math. Z. 250 (2005), 731-744.
9. B. E. Forrest, E. Samei, and N. Spronk, Weak amenability of Fourier algebras on compact groups, Indiana Univ. Math. J. 58 (2009), 1379-1394.
10. 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., ibid. 50 (2001), 1217-1240.
11. F. Ghahramani and R. Stokke, Approximate amenability and pseudo-amenability of the Fourier algebra, ibid. 56 (2007), 909-930.
12. N. Groenbaek, A characterization of weakly amenable Banach algebras, Studia Math. 94 (1989), 149-162.
13. C. S. Herz, Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble) 23 (1973), 91-123.
14. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis II, Grundlehren Math. Wiss. 152, Springer, New York, 1970.
15. -, -, Abstract Harmonic Analysis I, 2nd ed., Grundlehren Math. Wiss. 115, Springer, New York, 1979.
16. B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).
17. -, Non-amenability of the Fourier algebra of a compact group, J. London Math. Soc. 50 (1994), 361-374.
18. A. Ya. Khelemskiǐ, Flat Banach modules and amenable algebras, Trudy Moskov. Mat. Obshch. 47 (1982), 179-218 (in Russian);
19. English transi.: Trans. Moscow Math. Soc. 1985, 199-244.
20. V. Losert, On tensor products of Fourier algebras, Arch. Math. (Basel) 43 (1984), 370-372.
21. D. Montgomery and L. Zippin, Topological Transformation Groups, 4th ed., Interscience Tracts Pure and Appl. Math. 1, Wiley, New York, 1966.
22. C. C. Moore, Groups with finite dimensional irreducible representations, Trans. Amer. Math. Soc. 166 (1972), 401-410.
23. T. W. Palmer, Banach Algebras and the General Theory of *-algebras. Volume II. *-algebras, Encyclopedia Math. Appl. 79, Cambridge Univ. Press, Cambridge, 2001.
24. B. D. Park and E. Samei, Smooth and weak synthesis of the anti-diagonal in Fourier algebras of Lie groups, J. Lie Theory, accepted; arXiv:0809.2806vl.
25. R. J. Plymen, Fourier algebra of a compact Lie group, arXiv:math.FA/0104018.
26. Z.-J. Ruan, The operator amenability of A(G), Amer. J. Math. 117 (1995), 1449-1474.
27. V. Runde, Lectures on Amenability, Lecture Notes in Math. 1774, Springer, Berlin, 2002.
28. E. Samei, Bounded and completely bounded local derivations from certain commutative semisimple Banach algebras, Proc. Amer. Math. Soc. 133 (2005), 229-238.
29. -, Hyper-Tauberian algebras and weak amenability of Figà-Talamanca - Herz algebras, J. Funct. Anal. 231 (2006), 195-220.
30. N. Spronk, Operator weak amenability of the Fourier algebra, Proc. Amer. Math. Soc. 130 (2002), 3609-3617.
31. -, Operator space structure on Feichtinger's Segal algebra, J. Funct. Anal. 248 (2007), 152-174.
32. N. Spronk and L. Turowska, Spectral synthesis and operator synthesis for compact groups, J. London Math. Soc. (2) 66 (2002), 361-376.
33. M. Takesaki and N. Tatsuuma, Duality and subgroups, II, J. Funct. Anal. 11 (1972), 184-190.
34. N. Th. Varopoulos, Tensor algebras and harmonic analysis, Acta Math. 119 (1967), 51-112.