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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lineability and spaceability for the weak form of Peano’s theorem and vector-valued sequence spaces
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by Cleon S. Barroso, Geraldo Botelho, Vinícius V. Fávaro and Daniel Pellegrino PDF
Proc. Amer. Math. Soc. 141 (2013), 1913-1923 Request permission

Abstract:

Two new applications of a technique for spaceability are given in this paper. For the first time this technique is used in the investigation of the algebraic genericity property of the weak form of Peano’s theorem on the existence of solutions of the ODE $u’=f(u)$ on $c_0$. The space of all continuous vector fields $f$ on $c_0$ is proved to contain a closed $\mathfrak {c}$-dimensional subspace formed by fields $f$ for which, except for the null field, the weak form of Peano’s theorem fails to be true. The second application generalizes known results on the existence of closed $\mathfrak {c}$-dimensional subspaces inside certain subsets of $\ell _p(X)$-spaces, $0 < p < \infty$, to the existence of closed subspaces of maximal dimension inside such subsets.
References
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Additional Information
  • Cleon S. Barroso
  • Affiliation: Departamento de Matemática, Campus do Pici, Universidade Federal do Ceará, 60.455-760 Fortaleza, Brazil
  • Email: cleonbar@mat.ufc.br
  • Geraldo Botelho
  • Affiliation: Faculdade de Matemática, Universidade Federal de Uberlândia, 38.400-902, Uberlândia, Brazil
  • MR Author ID: 638411
  • Email: botelho@ufu.br
  • Vinícius V. Fávaro
  • Affiliation: Faculdade de Matemática, Universidade Federal de Uberlândia, 38.400-902, Uberlândia, Brazil
  • MR Author ID: 843580
  • Email: vvfavaro@gmail.com
  • Daniel Pellegrino
  • Affiliation: Departamento de Matemática, Universidade Federal da Paraíba, 58.051-900, João Pessoa, Brazil
  • Email: pellegrino@pq.cnpq.br, dmpellegrino@gmail.com
  • Received by editor(s): June 2, 2011
  • Received by editor(s) in revised form: September 24, 2011
  • Published electronically: December 28, 2012
  • Additional Notes: The first author was supported by CNPq Grant 307210/2009-0.
    The second author was supported by CNPq Grant 306981/2008-4.
    The third author was supported by FAPEMIG Grant CEX-APQ-00208-09.
    The fourth author was supported by CNPq Grant 301237/2009-3 and CAPES-NF
  • Communicated by: Michael T. Lacey
  • © Copyright 2012 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 1913-1923
  • MSC (2010): Primary 15A03, 46B45, 34A12
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11466-2
  • MathSciNet review: 3034418