On the Bishop–Phelps–Bollobás theorem for multilinear mappings

Sheldon Dantas, Domingo García, Sun Kwang Kim, Han Ju Lee, Manuel Maestre

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the Bishop–Phelps–Bollobás property and the Bishop–Phelps–Bollobás property for numerical radius. Our main aim is to extend some known results about norm or numerical radius attaining operators to multilinear and polynomial cases. We characterize the pair (ℓ1(X),Y) to have the BPBp for bilinear forms and prove that on L1(μ) the numerical radius and the norm of a multilinear mapping are the same. We also show that L1(μ) fails the BPBp-nu for multilinear mappings although L1(μ) satisfies it in the operator case for every measure μ.

Original languageEnglish
Pages (from-to)406-431
Number of pages26
JournalLinear Algebra and Its Applications
Volume532
DOIs
StatePublished - 1 Nov 2017

Keywords

  • Bilinear forms
  • Bishop–Phelps theorem
  • Bishop–Phelps–Bollobás property
  • Norm attaining

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