Absolute Schauder Decompositions and Linearization of Holomorphic Mappings of Bounded Type

  • Geraldo Botelho

    Universidade Federal de Uberlândia, Brazil
  • Vinícius V. Fávaro

    Universidade Federal de Uberlândia, Brazil
  • Jorge Mujica

    Universidade Estadual de Campinas, Brazil
Absolute Schauder Decompositions and Linearization of Holomorphic Mappings of Bounded Type cover

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Abstract

This paper has a twofold purpose: (i) to prove that the linearization of a holomorphic function of bounded type can be represented by means of the linearizations of its derivatives; (ii) to characterize when the identity operator on the predual of the space of holomorphic functions of bounded type on a balanced open subset of a Banach space belongs to a given closed operator ideal. These two results rely on the existence of an -absolute Schauder decomposition for .

Cite this article

Geraldo Botelho, Vinícius V. Fávaro, Jorge Mujica, Absolute Schauder Decompositions and Linearization of Holomorphic Mappings of Bounded Type. Publ. Res. Inst. Math. Sci. 55 (2019), no. 3, pp. 651–664

DOI 10.4171/PRIMS/55-3-6