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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.

Sous-espaces privilégiés d'un polycylindre

Geneviève Pourcin (1975)

Annales de l'institut Fourier

Cet article précise la notion de privilège introduite par A. Douady. Un sous-espace privilégié d’un polycylindre K est défini par un idéal fermé de l’algèbre des fonctions continues sur K et holomorphes sur K ˙ , cet idéal étant supposé de résolution finie.Les sous-espaces privilégiés d’un polycylindre fixé sont classés par un espace analytique banachique, “une grassmannienne”, introduit par A. Douady et dont on donne ici la propriété universelle.Pour cela on montre que la notion de privilège est locale...

Space of Baire functions. I

J. E. Jayne (1974)

Annales de l'institut Fourier

Several equivalent conditions are given for the existence of real-valued Baire functions of all classes on a type of K -analytic spaces, called disjoint analytic spaces, and on all pseudocompact spaces. The sequential stability index for the Banach space of bounded continuous real-valued functions on these spaces is shown to be either 0 , 1 , or Ω (the first uncountable ordinal). In contrast, the space of bounded real-valued Baire functions of class 1 is shown to contain closed linear subspaces with index...

Spaces defined by the level function and their duals

Gord Sinnamon (1994)

Studia Mathematica

The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of L p . These domains are shown to be Banach spaces which, although closely tied to L p spaces, are not reflexive. A related construction is given which characterizes their dual spaces.

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