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Linearization of multipolynomials and applications

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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.

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Authors and Affiliations

  1. Faculdade de Matemática, Universidade Federal de Uberlândia, Uberlândia, 38400-902,, Brazil

    Geraldo Botelho & Ewerton R. Torres

  2. IMECC-UNICAMP, Universidade Estadual de Campinas, São Paulo, 13083-859,, Brazil

    Thiago Velanga

  3. Departamento de Matemática, Universidade Federal de Rondônia, Porto Velho, 76801-059,, Brazil

    Thiago Velanga

Authors
  1. Geraldo Botelho
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  2. Ewerton R. Torres
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  3. Thiago Velanga
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Corresponding author

Correspondence to Geraldo Botelho.

Additional information

Geraldo Botelho: Supported by CNPq Grant 305958/2014-3 and Fapemig Grant PPM-00450-17. Ewerton R. Torres: Supported by a CAPES postdoctoral scholarship. Thiago Velanga: Supported by CAPES Grant 23038.002511/2014-48 and FAPERO Grant 01133100023-0000.41/2014.

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Botelho, G., Torres, E.R. & Velanga, T. Linearization of multipolynomials and applications. Arch. Math. 110, 605–615 (2018). https://doi.org/10.1007/s00013-018-1161-5

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  • DOI: https://doi.org/10.1007/s00013-018-1161-5

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