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Unitary sequences and classes of barrelledness.

Manuel López Pellicer, Salvador Moll (2003)

RACSAM

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.

Unordered Baire-like spaces without local convexity.

Jerzy Kakol, Walter Roelcke (1992)

Collectanea Mathematica

The aim of the present paper is to study the class of tvs which we define by ommiting the word increasing in the definition of *-suprabarrelled spaces. We prove that the product of Baire tvs is *-UBL and hence the class of *-UBL spaces is stricty larger than the class of Baire spaces.

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