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Strongly factorable multilinear operators on Banach spaces

Volume 154 / 2018

Geraldo Botelho, Ewerton R. Torres Colloquium Mathematicum 154 (2018), 15-30 MSC: Primary 47L22, 46G25, 46B28, 46A32; Secondary 47L20, 47B10. DOI: 10.4064/cm7269-12-2017 Published online: 18 June 2018

Abstract

We prove that for every ideal $\cal M$ of multilinear operators on Banach spaces there exists an ideal ${\cal M}^{\rm fac}$ such that every $n$-linear operator $A$ in ${\cal M}^{\rm fac}$ is strongly $\cal M$-factorable in the sense that it factors through multilinear operators in $\cal M$ with respect to any partition of $\{1, \ldots ,n\}$. We compute ${\cal M}^{\rm fac}$ for some important ideals ${\cal M}$ and we show that the passage from $\cal M$ to ${\cal M}^{\rm fac}$ is advantageous in the sense that ${\cal M}^{\rm fac}$ enjoys some properties that ${\cal M}$ may not enjoy.

Authors

  • Geraldo BotelhoFaculdade de Matemática
    Universidade Federal de Uberlândia
    38.400-902, Uberlândia, Brazil
    e-mail
  • Ewerton R. TorresFaculdade de Matemática
    Universidade Federal de Uberlândia
    38.400-902, Uberlândia, Brazil
    e-mail

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