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Norm Attaining Arens Extensions on ℓ1

Author

Listed:
  • Javier Falcó
  • Domingo García
  • Manuel Maestre
  • Pilar Rueda

Abstract

We study norm attaining properties of the Arens extensions of multilinear forms defined on Banach spaces. Among other related results, we construct a multilinear form on ℓ1 with the property that only some fixed Arens extensions determined a priori attain their norms. We also study when multilinear forms can be approximated by ones with the property that only some of their Arens extensions attain their norms.

Suggested Citation

Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:315641
DOI: 10.1155/2014/315641
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