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Archiv der Mathematik

, Volume 110, Issue 6, pp 605–615 | Cite as

Linearization of multipolynomials and applications

  • Geraldo BotelhoEmail author
  • Ewerton R. Torres
  • Thiago Velanga
Article
  • 47 Downloads

Abstract

We prove that every multipolynomial between Banach spaces is the composition of a canonical multipolynomial with a linear operator, and that this correspondence establishes an isometric isomorphism between the spaces of multipolynomials and linear operators. Applications to composition ideals of multipolynomials and to multipolynomials that are of finite rank, approximable, compact, and weakly compact are provided.

Keywords

Banach spaces Multipolynomials Linearization Projective tensor product Compact and weakly compact operators 

Mathematics Subject Classification

46G25 47H60 47L22 46M05 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Geraldo Botelho
    • 1
    Email author
  • Ewerton R. Torres
    • 1
  • Thiago Velanga
    • 2
    • 3
  1. 1.Faculdade de MatemáticaUniversidade Federal de UberlândiaUberlândiaBrazil
  2. 2.IMECC-UNICAMPUniversidade Estadual de CampinasSão PauloBrazil
  3. 3.Departamento de MatemáticaUniversidade Federal de RondôniaPorto VelhoBrazil

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