# Normed barrelled spaces

Banach Center Publications (2000)

- Volume: 53, Issue: 1, page 205-210
- ISSN: 0137-6934

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topStuart, Christopher. "Normed barrelled spaces." Banach Center Publications 53.1 (2000): 205-210. <http://eudml.org/doc/209076>.

@article{Stuart2000,

abstract = {In this paper we present a general “gliding hump” condition that implies the barrelledness of a normed vector space. Several examples of subspaces of $l^1$ 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]).},

author = {Stuart, Christopher},

journal = {Banach Center Publications},

keywords = {normed barrelled spaces; space of Pettis integrable functions},

language = {eng},

number = {1},

pages = {205-210},

title = {Normed barrelled spaces},

url = {http://eudml.org/doc/209076},

volume = {53},

year = {2000},

}

TY - JOUR

AU - Stuart, Christopher

TI - Normed barrelled spaces

JO - Banach Center Publications

PY - 2000

VL - 53

IS - 1

SP - 205

EP - 210

AB - In this paper we present a general “gliding hump” condition that implies the barrelledness of a normed vector space. Several examples of subspaces of $l^1$ 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]).

LA - eng

KW - normed barrelled spaces; space of Pettis integrable functions

UR - http://eudml.org/doc/209076

ER -

## References

top- [1] G. Bennett, A new class of sequence spaces with applications in summability theory, J. Reine Angew. Math. 266 (1974), 49-75. Zbl0277.46012
- [2] G. Bennett, Some inclusion theorems for sequence spaces, Pacific J. Math.64 (1973), 17-30.
- [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. Zbl0747.46026
- [4] W. Ruckle, The strong ϕ topology on symmetric sequence spaces, Canad. J. Math. 37 (1985), 1112-1133. Zbl0571.46006
- [5] W. Ruckle, FK spaces in which the sequence of coordinate functionals is bounded, Canad. J. Math. (1973), 973-978. Zbl0267.46008
- [6] W. Ruckle and S. Saxon, Generalized sectional convergence and multipliers, J. Math. Analysis and Appl. 193 (1995), 680-705. Zbl0881.46010
- [7] S. Saxon, Some normed barrelled spaces which are not Baire, Math. Ann. 209 (1974), 153-160. Zbl0295.46004
- [8] C. Stuart, Dense barrelled subspaces of Banach spaces, Collect. Math. 47 (1996), 137-143. Zbl0859.46004
- [9] C. Swartz, phIntroduction to Functional Analysis, Marcel Dekker, 1992.

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