Displaying similar documents to “CS-barrelled spaces.”

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. ...

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.

On nonbornological barrelled spaces

Manuel Valdivia (1972)

Annales de l'institut Fourier

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If E is the topological product of a non-countable family of barrelled spaces of non-nulle dimension, there exists an infinite number of non-bornological barrelled subspaces of E . The same result is obtained replacing “barrelled” by “quasi-barrelled”.