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Displaying similar documents to “Metrizable [normable] (LF)-spaces and two classical problems in Fréchet [Banach] spaces”

Some examples on quasi-barrelled spaces

Manuel Valdivia (1972)

Annales de l'institut Fourier

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The three following examples are given: a bornological space containing a subspace of infinite countable codimension which is not quasi-barrelled, a quasi-barrelled 𝒟 ℱ -space containing a subspace of infinite countable codimension which is not 𝒟 ℱ -space, and bornological barrelled space which is not inductive limit of Baire space.

Unitary sequences and classes of barrelledness.

Manuel López Pellicer, Salvador Moll (2003)

RACSAM

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It is well known that some dense subspaces of a barrelled space could be not barrelled. Here we prove that dense subspaces of l∞ (Ω, X) are barrelled (unordered Baire-like or p?barrelled) spaces if they have ?enough? subspaces with the considered barrelledness property and if the normed space X has this barrelledness property. These dense subspaces are used in measure theory and its barrelledness is related with some sequences of unitary vectors. ...