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Ciesielski and Franklin systems

Gegham G. Gevorkyan (2006)

Banach Center Publications

A short survey of results on classical Franklin system, Ciesielski systems and general Franklin systems is given. The principal role of the investigations of Z. Ciesielski in the development of these three topics is presented. Recent results on general Franklin systems are discussed in more detail. Some open problems are posed.

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...

Compact homomorphisms between algebras of analytic functions

Richard Aron, Pablo Galindo, Mikael Lindström (1997)

Studia Mathematica

We prove that every weakly compact multiplicative linear continuous map from H ( D ) into H ( D ) is compact. We also give an example which shows that this is not generally true for uniform algebras. Finally, we characterize the spectra of compact composition operators acting on the uniform algebra H ( B E ) , where B E is the open unit ball of an infinite-dimensional Banach space E.

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