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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.
López Pellicer, Manuel, and Moll, Salvador. "Unitary sequences and classes of barrelledness.." RACSAM 97.3 (2003): 367-376. <http://eudml.org/doc/40989>.
@article{LópezPellicer2003, abstract = {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.}, author = {López Pellicer, Manuel, Moll, Salvador}, journal = {RACSAM}, keywords = {Espacios lineales topológicos; Espacio tonelado; Disco de Banach; Espacios de Baire; Espacio bornológico; -barrelled spaces; dense barrelled subspaces; unordered Baire-like spaces; function spaces}, language = {eng}, number = {3}, pages = {367-376}, title = {Unitary sequences and classes of barrelledness.}, url = {http://eudml.org/doc/40989}, volume = {97}, year = {2003}, }
TY - JOUR AU - López Pellicer, Manuel AU - Moll, Salvador TI - Unitary sequences and classes of barrelledness. JO - RACSAM PY - 2003 VL - 97 IS - 3 SP - 367 EP - 376 AB - 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. LA - eng KW - Espacios lineales topológicos; Espacio tonelado; Disco de Banach; Espacios de Baire; Espacio bornológico; -barrelled spaces; dense barrelled subspaces; unordered Baire-like spaces; function spaces UR - http://eudml.org/doc/40989 ER -