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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 80, Issue 3
  • June 2006, pp. 317-333

Relative amenability and the non-amenability of B(l1)

  • C. J. Read (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788700014038
  • Published online: 01 April 2009
Abstract
Abstract

In this paper we begin with a short, direct proof that the Banach algebra B(l1) is not amenable. We continue by showing that various direct sums of matrix algebras are not amenable either, for example the direct sum of the finite dimensional algebras is no amenable for 1 ≤ p ≤ ∞, p ≠ 2. Our method of proof naturally involves free group algebras, (by which we mean certain subalgebras of B(X) for some space X with symmetric basis—not necessarily X = l2) and we introduce the notion of ‘relative amenability’ of these algebras.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]B. Bollobsá Random graphs (Academic Press, London, 1985).

[2]A. Connes Classification of injective factors’, Ann. of Math. (2) 104 (1976), 73115.

[4]U. Haagerup All nuclear C*-algebras are amenable’, Invent. Math. 74 (1983), 93116.

[5]N. Ozawa A note on non-amenability of B(lp) for p = 1, 2’, Internat. J. Math. 15 (2004), 557565.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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