Amenability of Banach and C*-algebras on locally compact groups
Lau, A. ; Loy, R. ; Willis, G.
Studia Mathematica, Tome 119 (1996), p. 161-178 / Harvested from The Polish Digital Mathematics Library

Several results are given about the amenability of certain algebras defined by locally compact groups. The algebras include the C*-algebras and von Neumann algebras determined by the representation theory of the group, the Fourier algebra A(G), and various subalgebras of these.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:216292
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     title = {Amenability of Banach and C*-algebras on locally compact groups},
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     volume = {119},
     year = {1996},
     pages = {161-178},
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Lau, A.; Loy, R.; Willis, G. Amenability of Banach and C*-algebras on locally compact groups. Studia Mathematica, Tome 119 (1996) pp. 161-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv119i2p161bwm/

[00000] [1] A. Bérlanger and B. E. Forrest, Geometric properties of coefficient function spaces determined by unitary representations of a locally compact group, J. Math. Anal. Appl. 193 (1995), 390-405. | Zbl 0854.43010

[00001] [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, New York, 1973. | Zbl 0271.46039

[00002] [3] G. Brown and W. Moran, Point derivations on M(G), Bull. London Math. Soc. 8 (1976), 57-64.

[00003] [4] J. W. Bunce, Finite operators and amenable C*-algebras, Proc. Amer. Math. Soc. 56 (1976), 145-151. | Zbl 0343.46039

[00004] [5] M. D. Choi and E. Effros, Nuclear C*-algebras and the approximation property, Amer. J. Math. 100 (1978), 61-80. | Zbl 0397.46054

[00005] [6] E. Christensen and A. M. Sinclair, Completely bounded isomorphisms of injective von Neumann algebras, Proc. Edinburgh Math. Soc. 32 (1989), 317-327. | Zbl 0651.46059

[00006] [7] C.-H. Chu and B. Iochum, The Dunford-Pettis property in C*-algebras, Studia Math. 97 (1990), 59-64. | Zbl 0734.46034

[00007] [8] C.-H. Chu, B. Iochum and S. Watanabe, C*-algebras with the Dunford-Pettis property, in: Function Spaces, K. Jarosz (ed.), Dekker, New York, 1992, 67-70. | Zbl 0817.46054

[00008] [9] A. Connes, On the cohomology of operator algebras, J. Funct. Anal. 28 (1978), 248-253. | Zbl 0408.46042

[00009] [10] M. Cowling and P. Rodway, Restrictions of certain function spaces to closed subgroups of locally compact groups, Pacific J. Math. 80 (1979), 91-104. | Zbl 0417.43002

[00010] [11] P. C. Curtis, Jr., and R. J. Loy, The structure of amenable Banach algebras, J. London Math. Soc. (2) 40 (1989), 89-104. | Zbl 0698.46043

[00011] [12] J. Duncan and S. A. R. Hosseiniun, The second dual of a Banach algebra, Proc. Roy. Soc. Edinburgh Sect. A 84 (1979), 309-325. | Zbl 0427.46028

[00012] [13] J. Duncan and I. Namioka, Amenability of inverse semigroups and their semigroup algebras, ibid. 80 (1978), 309-321. | Zbl 0393.22004

[00013] [14] J. Duncan and A. L. T. Paterson, Amenability for discrete convolution semigroup algebras, Math. Scand. 66 (1990), 141-146. | Zbl 0748.46027

[00014] [15] P. Eymard, L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181-236. | Zbl 0169.46403

[00015] [16] E. Formanek, The type I part of the regular representation, Canad. J. Math. 26 (1974), 1086-1089. | Zbl 0253.43012

[00016] [17] F. Ghahramani and A. T.-M. Lau, Multipliers and ideals in second conjugate algebras related to group algebras, J. Funct. Anal. 132 (1995), 170-191. | Zbl 0832.22007

[00017] [18] F. Ghahramani, R. J. Loy and G. A. Willis, Amenability and weak amenability of second conjugate Banach algebras, Proc. Amer. Math. Soc., to appear. | Zbl 0851.46035

[00018] [19] E. Granirer, Weakly almost periodic and uniformly continuous functions on the Fourier algebra of any locally compact group, Trans. Amer. Math. Soc. 189 (1974), 371-382. | Zbl 0292.43015

[00019] [20] N. Grønbæk, Amenability of discrete convolution algebras, the commutative case, Pacific. J. Math. 143 (1990), 243-249. | Zbl 0662.43002

[00020] [21] U. Haagerup, All nuclear C*-algebras are amenable, Invent. Math. 74 (1983), 305-319. | Zbl 0529.46041

[00021] [22] M. Hamana, On linear topological properties of some C*-algebras, Tôhoku Math. J. 29 (1977), 157-163. | Zbl 0346.46045

[00022] [23] A. Ya. Helemskii, The Homology of Banach and Topological Algebras, Kluwer, Dordrecht, 1989.

[00023] [24] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1967. | Zbl 0217.07201

[00024] [25] M. F. Hutchinson, Non-tall compact groups admit infinite Sidon sets, J. Austral. Math. Soc. 23 (1977), 467-475. | Zbl 0368.43005

[00025] [26] I. M. Isaacs and D. S. Passman, Groups with representations of bounded degree, Canad. J. Math. 16 (1964), 299-309. | Zbl 0124.26701

[00026] [27] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972). | Zbl 0256.18014

[00027] [28] B. E. Johnson, Non-amenability of the Fourier algebra of a compact group, J. London Math. Soc. (2) 50 (1994), 361-374. | Zbl 0829.43004

[00028] [29] A. Kaniuth, On the conjugate representation of a locally compact group, Math. Z. 202 (1989), 275-288. | Zbl 0681.22005

[00029] [30] A. T.-M. Lau, Uniformly continuous functionals on the Fourier algebra of any locally compact group, Trans. Amer. Math. Soc. 251 (1979), 39-59. | Zbl 0436.43007

[00030] [31] A. T.-M. Lau, The second conjugate algebra of the Fourier algebra of a locally compact group, ibid. 267 (1981), 53-63. | Zbl 0489.43006

[00031] [32] A. T.-M. Lau and V. Losert, The C*-algebra generated by operators with compact support on a locally compact group, J. Funct. Anal. 112 (1993), 1-30. | Zbl 0788.22006

[00032] [33] A. T.-M. Lau and R. J. Loy, Amenability of convolution algebras, Math. Scand., to appear. | Zbl 0880.46038

[00033] [34] A. T.-M. Lau and A. L. T. Paterson, Inner amenable locally compact groups, Trans. Amer. Math. Soc. 325 (1991), 155-169. | Zbl 0718.43002

[00034] [35] J. R. McMullen and J. F. Price, Rudin-Shapiro sequences for arbitrary compact groups, J. Austral. Math. Soc. 22 (1976), 421-430. | Zbl 0342.43018

[00035] [36] C. C. Moore, Groups with finite dimensional irreducible representations, Trans. Amer. Math. Soc. 166 (1972), 401-410. | Zbl 0236.22010

[00036] [37] T. W. Palmer, Classes of non-abelian, non-compact locally compact groups, Rocky Mountain J. Math. 8 (1973), 683-741.

[00037] [38] A. L. T. Paterson, Amenability, Math. Surveys Monographs 29, Amer. Math. Soc., Providence, 1988.

[00038] [39] G. K. Pederson, C*-Algebras and their Automorphism Groups, Academic Press, London, 1979. | Zbl 0437.65048

[00039] [40] P. F. Renauld, Invariant means on a class of von Neumann algebras, Trans. Amer. Math. Soc. 170 (1972), 285-291.

[00040] [41] R. R. Smith and D. P. Williams, The decomposition property for C*-algebras, J. Operator Theory 16 (1986), 51-74. | Zbl 0633.46058

[00041] [42] A. Szankowski, B (H) does not have the approximation property, Acta Math. 147 (1981), 89-108. | Zbl 0486.46012

[00042] [43] M. Takesaki, Theory of Operator Algebras I, Springer, New York, 1979.

[00043] [44] K. Taylor, The type structure of the regular representation of a locally compact group, Math. Ann. 222 (1976), 211-214. | Zbl 0318.43005

[00044] [45] E. Thoma, Eine Charakterisierung diskreter Gruppen vom typ 1, Invent. Math. 6 (1968), 190-196. | Zbl 0169.03802

[00045] [46] S. Wassermann, On tensor products of certain group C*-algebras, J. Funct. Anal. 23 (1976), 239-254. | Zbl 0358.46040

[00046] [47] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Univ. Press, Cambridge, 1991. | Zbl 0724.46012