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Sous-espaces fermés de séries universelles sur un espace de Fréchet

Quentin Menet — 2011

Studia Mathematica

We improve a result of Charpentier [Studia Math. 198 (2010)]. We prove that even on Fréchet spaces with a continuous norm, the existence of only one restrictively universal series implies the existence of a closed infinite-dimensional subspace of restrictively universal series.

Closed universal subspaces of spaces of infinitely differentiable functions

Stéphane Charpentier; Quentin Menet; Augustin Mouze — 2014

Annales de l’institut Fourier

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...

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