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Israel Journal of Mathematics

, Volume 87, Issue 1–3, pp 289–324 | Cite as

Amenability of Banach algebras of compact operators

  • N. Grønbæk
  • B. E. Johnson
  • G. A. Willis
Article

Abstract

In this paper we study conditions on a Banach spaceX that ensure that the Banach algebraК(X) of compact operators is amenable. We give a symmetrized approximation property ofX which is proved to be such a condition. This property is satisfied by a wide range of Banach spaces including all the classical spaces. We then investigate which constructions of new Banach spaces from old ones preserve the property of carrying amenable algebras of compact operators. Roughly speaking, dual spaces, predual spaces and certain tensor products do inherit this property and direct sums do not. For direct sums this question is closely related to factorization of linear operators. In the final section we discuss some open questions, in particular, the converse problem of what properties ofX are implied by the amenability ofК(X).

Keywords

Banach Space Tensor Product Banach Algebra Approximation Property Approximate Identity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1994

Authors and Affiliations

  • N. Grønbæk
    • 1
  • B. E. Johnson
    • 2
  • G. A. Willis
    • 3
  1. 1.Matematisk InstitutKøbenhavn ØDenmark
  2. 2.Department of Mathematics and StatisticsUniversity of Newcastle upon TyneNewcastle upon TyneEngland
  3. 3.Department of MathematicsThe University of NewcastleAustralia

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