On the closed subspaces of universal series in Banach spaces and Fréchet spaces
We prove, in a general framework, the existence of a closed infinite-dimensional subspace consisting of universal series.
Closed universal subspaces of spaces of infinitely differentiable functions
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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