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Banach spaces of homogeneous polynomials without the approximation property

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Abstract

We present simple proofs that spaces of homogeneous polynomials on L p [0, 1] and ℓ p provide plenty of natural examples of Banach spaces without the approximation property. By giving necessary and sufficient conditions, our results bring to completion, at least for an important collection of Banach spaces, a circle of results begun in 1976 by R. Aron and M. Schottenloher (1976).

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Authors and Affiliations

  1. School of Mathematical Sciences, University College Dublin, Science Centre North, Belfield, Dublin 4, Ireland

    Seán Dineen

  2. Department of Mathematics, Universidade Estadual de Campinas, Rua Sergio Buarque de Holanda 651, 13083-859, Campinas, São Paulo, Brazil

    Jorge Mujica

Authors
  1. Seán Dineen
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  2. Jorge Mujica
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Correspondence to Seán Dineen.

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Dedicated to the memory of Pierre Lelong (1912–2011)

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Dineen, S., Mujica, J. Banach spaces of homogeneous polynomials without the approximation property. Czech Math J 65, 367–374 (2015). https://doi.org/10.1007/s10587-015-0181-6

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  • DOI: https://doi.org/10.1007/s10587-015-0181-6

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