Closed universal subspaces of spaces of infinitely differentiable functions

Stéphane Charpentier[1]; Quentin Menet[2]; Augustin Mouze[3]

  • [1] Laboratoire Paul Painlevé, UMR 8524, Université Lille 1, Cité Scientifique, 59650 Villeneuve d’Ascq
  • [2] Institut de Mathématique, Université de Mons, 20 Place du Parc, 7000 Mons, Belgique
  • [3] Laboratoire Paul Painlevé, UMR 8524, Current address: École Centrale de Lille, Cité Scientifique, BP48, 59651 Villeneuve d’Ascq cedex

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 1, page 297-325
  • ISSN: 0373-0956

Abstract

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We exhibit the first examples of Fréchet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series. We consider classical Fréchet spaces of infinitely differentiable functions which do not admit a continuous norm. Furthermore, this leads us to establish some more general results for sequences of operators acting on Fréchet spaces with or without a continuous norm. Additionally, we give a characterization of the existence of a closed subspace of universal series in the Fréchet space 𝕂 ℕ .

How to cite

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Charpentier, Stéphane, Menet, Quentin, and Mouze, Augustin. "Closed universal subspaces of spaces of infinitely differentiable functions." Annales de l’institut Fourier 64.1 (2014): 297-325. <http://eudml.org/doc/275666>.

@article{Charpentier2014,
abstract = {We exhibit the first examples of Fréchet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series. We consider classical Fréchet spaces of infinitely differentiable functions which do not admit a continuous norm. Furthermore, this leads us to establish some more general results for sequences of operators acting on Fréchet spaces with or without a continuous norm. Additionally, we give a characterization of the existence of a closed subspace of universal series in the Fréchet space $\mathbb\{K\}^\{\mathbb\{N\}\}.$},
affiliation = {Laboratoire Paul Painlevé, UMR 8524, Université Lille 1, Cité Scientifique, 59650 Villeneuve d’Ascq; Institut de Mathématique, Université de Mons, 20 Place du Parc, 7000 Mons, Belgique; Laboratoire Paul Painlevé, UMR 8524, Current address: École Centrale de Lille, Cité Scientifique, BP48, 59651 Villeneuve d’Ascq cedex},
author = {Charpentier, Stéphane, Menet, Quentin, Mouze, Augustin},
journal = {Annales de l’institut Fourier},
keywords = {infinitely differentiable real functions; spaceability; universality; universal series; Taylor series},
language = {eng},
number = {1},
pages = {297-325},
publisher = {Association des Annales de l’institut Fourier},
title = {Closed universal subspaces of spaces of infinitely differentiable functions},
url = {http://eudml.org/doc/275666},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Charpentier, Stéphane
AU - Menet, Quentin
AU - Mouze, Augustin
TI - Closed universal subspaces of spaces of infinitely differentiable functions
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 1
SP - 297
EP - 325
AB - We exhibit the first examples of Fréchet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series. We consider classical Fréchet spaces of infinitely differentiable functions which do not admit a continuous norm. Furthermore, this leads us to establish some more general results for sequences of operators acting on Fréchet spaces with or without a continuous norm. Additionally, we give a characterization of the existence of a closed subspace of universal series in the Fréchet space $\mathbb{K}^{\mathbb{N}}.$
LA - eng
KW - infinitely differentiable real functions; spaceability; universality; universal series; Taylor series
UR - http://eudml.org/doc/275666
ER -

References

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