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

  • C. J. Read (a1)
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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References
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[1]Bollobsá B.Random graphs (Academic Press, London, 1985).
[2]Connes A.Classification of injective factors’, Ann. of Math. (2) 104 (1976), 73115.
[3]Dales H. G., Banach algebras and automatic continuity, London Mathematical Society Monographs, New Series 24 (Oxford University Press, New York, 2001).
[4]Haagerup U.All nuclear C*-algebras are amenable’, Invent. Math. 74 (1983), 93116.
[5]Ozawa N.A note on non-amenability of B(lp) for p = 1, 2’, Internat. J. Math. 15 (2004), 557565.
[6]Pisier G. ‘On Read's proof that B(l1) is not amenable’, in: Geometric aspects of functional analysis, Lecture Notes in Math. 1850 (Springer, Berlin, 2004).
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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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