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Semisimplicity of reflexive amenable operator algebras

Abstract

We prove that amenable and reflexive operator algebras are semisimple and are finite direct sums of simple Banach algebras of operators.

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Correspondence to Paulo R. Pinto.

Additional information

The second author was partially supported by the Fundação para a Ciência e a Tecnologia through the Program POCI 2010/FEDER.

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Harti, R.E., Pinto, P.R. Semisimplicity of reflexive amenable operator algebras. Arch. Math. 101, 129–133 (2013). https://doi.org/10.1007/s00013-013-0546-8

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Mathematics Subject Classification (2010)

  • Primary 46B10
  • 47L10
  • Secondary 46H20

Keywords

  • Banach algebra
  • Operator algebra
  • Amenable Banach algebra
  • Reflexive Banach algebra
  • Arens regular