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Amenability of Banach and C -algebras generated by unitary representations
Author(s):
Ross
Stokke
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1477-1487.
MSC (2000):
Primary 22D10, 22D25, 43A30
Posted:
December 18, 2007
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Abstract:
We study the amenability of a locally compact group in relation to the amenability properties of a variety of -algebras and (quantized/dual) Banach algebras naturally associated to a unitary representation of .
References:
-
- 1.
- G. Arsac, Sur l'espace de Banach engendr
par les coefficients d'une repr sentation unitaire, Publ. D p. Math. (Lyon) 13 (1976), 1 - 101. MR 0444833 (56:3180) - 2.
- E. B
dos, On the -algebra generated by the left regular representation of a locally compact group, Proc. Amer. Math. Soc. 120 (1994), 603-608. MR 1181157 (94d:22004) - 3.
- M.E.B. Bekka, Amenable unitary representations of locally compact groups, Invent. Math. 100 (1990), 383-401. MR 1047140 (91g:22007)
- 4.
- M.E.B. Bekka, A.T. Lau, and G. Schlichting, On invariant subalgebras of the Fourier-Stieltjes algebra of a locally compact group, Math. Ann. 294 (1992), 513-522. MR 1188135 (93k:43006)
- 5.
- B. Bekka, P. de la Harpe, and A. Valette, Khazdan's property (T), Manuscript.
- 6.
- D. Blecher, The standard dual of an operator space, Pacific J. Math. 153 (1992), no. 1, 15-30. MR 1145913 (93d:47083)
- 7.
- H.G. Dales, F. Ghahramani, and A. Ya. Helemskii, The amenability of measure algebras, J. London Math. Soc. (2) 66 (2002), no. 1, 213-226. MR 1911870 (2003c:43001)
- 8.
- J. Dixmier,
(translated from the French), North-Holland, 1977. MR 0458185 (56:16388) - 9.
- E.G. Effros and E. C. Lance, Tensor products of operator algebras, Adv. Math. 25 (1977), no. 1, 1-34. MR 0448092 (56:6402)
- 10.
- E.G. Effros and Z.-J. Ruan, Operator Spaces, Oxford University Press, 2000. MR 1793753 (2002a:46082)
- 11.
- P. Eymard, L'alg
bre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181-236. MR 0228628 (37:4208) - 12.
- P. Eymard, Moyennes invariantes et repr
sentations unitaire, Springer-Verlag, Berlin, 1972. MR 0447969 (56:6279) - 13.
- J.M.G. Fell and R.S. Doran, Representations of
-algebras, locally compact groups, and Banach -algebraic bundles, Vol. 1, Pure and Applied Mathematics, 125. Academic Press, Inc., Boston, MA, 1988. MR 936628 (90c:46001) - 14.
- B. Forrest, Fourier analysis on coset spaces, Rocky Mountain J. Math. 28, (1998), no. 1, 173-189. MR 1639849 (99h:43020)
- 15.
- F.P. Greenleaf, Invariant means on topological groups, New York, Van Nostrand, 1969. MR 0251549 (40:4776)
- 16.
- E. Kaniuth, On the conjugation representation of a locally compact group, Math. Z. 202 (1989), no. 2, 275-288. MR 1013090 (90k:22003)
- 17.
- E. Kaniuth and A.T. Lau, A separation property of positive definite functions on locally compact groups and applications to Fourier algebras, J. Funct. Anal. 175 (2000), no. 1, 89-110. MR 1774852 (2001m:43012)
- 18.
- E. Kaniuth and A. Markfort, On
-algebras associated to the conjugation representation of a locally compact group, Trans. Amer. Math. Soc. 347 (1995), 2595-2606. MR 1277118 (95i:22009) - 19.
- E.C. Lance, On nuclear
-algebras, J. Functional Analysis 12 (1973), 157-176. MR 0344901 (49:9640) - 20.
- A. T.-M. Lau and A.L.T. Paterson, Inner amenable locally compact groups, Trans. Amer. Math. Soc. 325(1991) 155-169. MR 1010885 (91h:43002)
- 21.
- Z.-J. Ruan, The operator amenability of
, Amer. J. Math. 117 (1995), 1449-1474. MR 1363075 (96m:43001) - 22.
- V. Runde, Lectures on amenability, Lecture Notes in Mathematics 1774. Springer-Verlag, Berlin-Heidelberg-New York, 2002. MR 1874893 (2003h:46001)
- 23.
- V. Runde and N. Spronk, Operator amenability of Fourier-Stieltjes algebras, Math. Proc. Cambridge Philos. Soc. 136 (2004), no. 3, 675-686. MR 2055055 (2005b:46106)
- 24.
- R. Stokke, Amenable representations and coefficient subspaces of Fourier-Stieltjes algebras, Math. Scand. 98 (2006), no. 2, 182-200. MR 2243701 (2007b:22006)
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Additional Information:
Ross
Stokke
Affiliation:
Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Canada R3B 2E9
Email:
r.stokke@uwinnipeg.ca
DOI:
10.1090/S0002-9939-07-09221-0
PII:
S 0002-9939(07)09221-0
Received by editor(s):
July 26, 2006
Posted:
December 18, 2007
Additional Notes:
This research was supported by NSERC grant 298444-04
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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