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Factorization of weakly continuous differentiable mappings

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Abstract

Given real Banach spaces X and Y, let C 1wbu (X, Y) be the space, introduced by R.M. Aron and J.B. Prolla, of C 1 mappings from X into Y such that the mappings and their derivatives are weakly uniformly continuous on bounded sets. We show that f ∈ C 1wbu (X, Y) if and only if f may be written in the form f = g ∘ S, where the intermediate space is normed, S is a precompact operator, and g is a Gâteaux differentiable mapping with some additional properties.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica Facoltà di Scienze, Università di Catania, Viale Andrea Doria 6, 95125, Catania, Italy

    Raffaella Cilia

  2. Departamento de Matemática Aplicada ETS de Ingenieros Industriales, Universidad Politécnica de Madrid, C. José Gutiérrez Abascal 2, 28006, Madrid, Spain

    Joaquín M. Gutiérrez

Authors
  1. Raffaella Cilia
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  2. Joaquín M. Gutiérrez
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Corresponding author

Correspondence to Raffaella Cilia.

Additional information

Both authors were supported in part by Dirección General de Investigación, MTM 2006-03531 (Spain). The first author was also supported by G.N.A.M.P.A (Italy).

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Cilia, R., Gutiérrez, J.M. Factorization of weakly continuous differentiable mappings. Bull Braz Math Soc, New Series 40, 371–380 (2009). https://doi.org/10.1007/s00574-009-0016-x

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  • DOI: https://doi.org/10.1007/s00574-009-0016-x

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