NA(L(n l1: l1))=NRA(L(n l1: l1))

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Abstract

Let n ≥ 2 and L(n E: E) denote the space of all continuous n-linear mappings from a Banach space E to itself. Let NA(L(n E: E)) denote the set of all norm attaining n-linear mappings in L(n E: E) and NRA(L(n E: E)) denote the set of all numerical radius attaining n-linear mappings in L(n E: E). In this paper we show that NA(L(n E: E))=NRA(L(n E: E)) if E = l1. We also characterize NA(L(n l1: l1)).

Original languageEnglish
Pages (from-to)769-775
Number of pages7
JournalActa Scientiarum Mathematicarum
Volume88
Issue number3-4
DOIs
StatePublished - Dec 2022

Keywords

  • norm attaining multilinear mappings
  • numerical radius attaining multilinear mappings

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