In this paper we present a general “gliding hump” condition that implies the barrelledness of a normed vector space. Several examples of subspaces of are shown to be barrelled using the theorem. The barrelledness of the space of Pettis integrable functions is also implied by the theorem (this was first shown in [3]).
@article{bwmeta1.element.bwnjournal-article-bcpv53z1p205bwm,
author = {Stuart, Christopher},
title = {Normed barrelled spaces},
journal = {Banach Center Publications},
volume = {51},
year = {2000},
pages = {205-210},
zbl = {0974.46003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv53z1p205bwm}
}
Stuart, Christopher. Normed barrelled spaces. Banach Center Publications, Tome 51 (2000) pp. 205-210. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv53z1p205bwm/
[000] [1] G. Bennett, A new class of sequence spaces with applications in summability theory, J. Reine Angew. Math. 266 (1974), 49-75. | Zbl 0277.46012
[001] [2] G. Bennett, Some inclusion theorems for sequence spaces, Pacific J. Math.64 (1973), 17-30.
[002] [3] L. Drewnowski, M. Florencio, and P. J. Paul, The space of Pettis integrable functions is barrelled, Proc. Amer. Math. Soc. 114 (1992), 687-694. | Zbl 0747.46026
[003] [4] W. Ruckle, The strong ϕ topology on symmetric sequence spaces, Canad. J. Math. 37 (1985), 1112-1133. | Zbl 0571.46006
[004] [5] W. Ruckle, FK spaces in which the sequence of coordinate functionals is bounded, Canad. J. Math. (1973), 973-978. | Zbl 0267.46008
[005] [6] W. Ruckle and S. Saxon, Generalized sectional convergence and multipliers, J. Math. Analysis and Appl. 193 (1995), 680-705. | Zbl 0881.46010
[006] [7] S. Saxon, Some normed barrelled spaces which are not Baire, Math. Ann. 209 (1974), 153-160. | Zbl 0295.46004
[007] [8] C. Stuart, Dense barrelled subspaces of Banach spaces, Collect. Math. 47 (1996), 137-143. | Zbl 0859.46004
[008] [9] C. Swartz, phIntroduction to Functional Analysis, Marcel Dekker, 1992.