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The Operator Biprojectivity of the Fourier Algebra

Published online by Cambridge University Press:  20 November 2018

Peter J. Wood
Peter J. Wood*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, email: pwood@uwaterloo.ca
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Abstract

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In this paper, we investigate projectivity in the category of operator spaces. In particular, we show that the Fourier algebra of a locally compact group $G$ is operator biprojective if and only if $G$ is discrete.

Keywords

13D0318G2543A9546L0722D99locally compact groupFourier algebraoperator spaceprojective
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 5 , 01 October 2002 , pp. 1100 - 1120
Copyright
Copyright © Canadian Mathematical Society 2002

References

[1] Arsac, G., Sur l'espace de Banach engendré par les coefficients d'une représentation unitaire. Publ. Dép. Math. (Lyon) 13 (1976), 1–101.Google Scholar
[2] Blecher, D. P., The standard dual of an operator space. Pacific J. Math. 153 (1992), 15–30.Google Scholar
[3] Blecher, D. P. and Paulsen, V. I., Tensor products of operator spaces. J. Funct. Anal. 99 (1991), 262–292.Google Scholar
[4] Cartan, H. and Eilenberg, S., Homological Algebra. Princeton University Press, Princeton, 1956.Google Scholar
[5] Curtis, P. C. and Loy, R. J., Amenable Banach algebras. J. London Math Soc. 40 (1989), 89–104.Google Scholar
[6] Effros, E. G. and Ruan, Z.-J., On the abstract characterization of operator spaces. Proc. Amer.Math. Soc. 119 (1990), 579–584.Google Scholar
[7] Effros, E. G. and Ruan, Z.-J., On approximation properties for operator spaces. Internat. J. Math. 1 (1990), 163–187.Google Scholar
[8] Effros, E. G. and Ruan, Z.-J., Operator convolution algebras: an approach to quantum groups. Preprint.Google Scholar
[9] Eymard, P., L'algèbre de Fourier d'un groupe localement compact. Bull. Soc. Math. France 92 (1964), 181–236.Google Scholar
[10] Forrest, B., Amenability and bounded approximate identities in ideals of A(G). Illinois J. Math. (1) 34 (1990), 1–25.Google Scholar
[11] Forrest, B. and Wood, P. J., Cohomology and the operator space structure of the Fourier algebra and its second dual. Indiana Univ.Math. J. (3) 50 (2001), 1217–1240.Google Scholar
[12] Johnson, B., Cohomology in Banach algebras. Mem. Amer.Math. Soc. 127, 1972.Google Scholar
[13] Khelemskii, A. Ya., Flat Banach modules and amenable algebras. Trans.Moscow Math. Soc. 47(1984) 179–218, 247; Amer. Math. Soc. Transl. (1985) 199–224.Google Scholar
[14] Khelemskii, A. Ya., The Homology of Banach and Topological Algebras. Mathematics and its Applications (Soviet Series) 41, Kluwer Academic Publishers, 1989.Google Scholar
[15] Khelemskii, A. Ya., Banach and Locally Convex Algebras. Oxford Science Publications, 1993.Google Scholar
[16] Kumar, A. and Sinclair, A. M., Equivalence of norms on operator space tensor products of C*algebras. Trans. Amer. Math. Soc. (5) 350 (1998), 2033–2048.Google Scholar
[17] Losert, V., Properties of groups without the property P1. Comment.Math. Helv. (3) 54 (1979), 133–139.Google Scholar
[18] MacLane, S., Homology. Springer-Verlag, 1963.Google Scholar
[19] Ruan, Z.-J., The operator amenability of A(G). Amer. J. Math. 117 (1995), 1449–1474.Google Scholar
[20] Ruan, Z.-J. and Xu, G., Splitting properties of operator bimodules and the operator amenability of Kac algebras. In: 16th Operator Theory Conference Proceedings, Theta Found. Bucharest, 1997, 193–216.Google Scholar
[21] Steiniger, H., Finite-dimensional extensions of Fourier algebras. Preprint.Google Scholar
[22] Taylor, J. L., Homology and cohomology for topological algebras. Advances in Math. 9 (1972), 137–182.Google Scholar
[23] Taylor, K., Geometry of the Fourier algebras and locally compact groups with atomic unitary representations. Math. Ann. (2) 262 (1983), 183–190.Google Scholar
[24] Wood, P. J., Complemented ideals in the Fourier algebra of a locally compact group. Proc. Amer.Math. Soc. (2) 128 (2000), 445–451.Google Scholar