Displaying similar documents to “A projective description of the simple scalar function 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. ...

Biduality in (LF)-spaces.

Klaus D. Bierstedt, José Bonet (2001)

RACSAM

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En la Sección 1 se pueban resultados abstractos sobre preduales y sobre bidualidad de espacios (LF). Sea E = ind E un espacio (LF), ponemos H = ind H para una sucesión de subespacios de Fréchet H de E con H ⊂ H. Investigamos bajo qué condiciones el espacio E es canónicamente (topológicamente isomorfo a) el bidual inductivo (H')' o (incluso) al bidual fuerte de H. Los resultados abstractos se aplican en la Sección 2, especialmente a espacios (LF) ponderados de funciones holomorfas, pero...

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 -space containing a subspace of infinite countable codimension which is not 𝒟 -space, and bornological barrelled space which is not inductive limit of Baire space.