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

Published online by Cambridge University Press:  09 April 2009

C. J. Read
Affiliation:
Faculty of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom, e-mail: read@maths.leeds.ac.uk
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Bollobsá, B.Random graphs (Academic Press, London, 1985).Google Scholar
[2]Connes, A.Classification of injective factors’, Ann. of Math. (2) 104 (1976), 73115.Google Scholar
[3]Dales, H. G., Banach algebras and automatic continuity, London Mathematical Society Monographs, New Series 24 (Oxford University Press, New York, 2001).Google Scholar
[4]Haagerup, U.All nuclear C*-algebras are amenable’, Invent. Math. 74 (1983), 93116.Google Scholar
[5]Ozawa, N.A note on non-amenability of B(lp) for p = 1, 2’, Internat. J. Math. 15 (2004), 557565.Google Scholar
[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).Google Scholar