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Amenability of algebras of approximable operators

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Abstract

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson’s space.

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Authors and Affiliations

  1. Department of Pure Mathematics, Queen’s University Belfast, Belfast, BT7 1NN, UK

    A. Blanco & N. Grønbæk

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  1. A. Blanco
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  2. N. Grønbæk
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Correspondence to A. Blanco.

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Blanco, A., Grønbæk, N. Amenability of algebras of approximable operators. Isr. J. Math. 171, 127–156 (2009). https://doi.org/10.1007/s11856-009-0044-7

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  • DOI: https://doi.org/10.1007/s11856-009-0044-7

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