J. Aust. Math. Soc.  81 (2006), 141-148
On symmetric ideals of multilinear mappings between Banach spaces

Geraldo Botelho
  Faculdade de Matemática
  Univ. Federal de Uberlandia
  38.400–902 Uberlandia
  Brazil
  botelho@ufu.br
and
Daniel M. Pellegrino
  Departamento de Matemática e Estatística
  Univ. Federal de Campina Grande
  58.109–970 Campina Grande
  Brazil
  dmp@dme.ufcg.edu.br


Abstract
In this paper we provide examples and counterexamples of symmetric ideals of multilinear mappings between Banach spaces and prove that if $\mathcal{I}_1, \dots, \mathcal{I}_n$ are operator ideals, then the ideals of multilinear mappings $\mathcal{L}(\mathcal{I}_1, \dots, \mathcal{I}_n)$ and $[\mathcal{I}_1, \dots, \mathcal{I}_n]$ are symmetric if and only if $\mathcal{I}_1 = \cdots = \mathcal{I}_n$.
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