Normed barrelled spaces

Christopher Stuart

Banach Center Publications (2000)

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

Abstract

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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]).

How to cite

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Stuart, 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

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  1. [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. [2] G. Bennett, Some inclusion theorems for sequence spaces, Pacific J. Math.64 (1973), 17-30. 
  3. [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. [4] W. Ruckle, The strong ϕ topology on symmetric sequence spaces, Canad. J. Math. 37 (1985), 1112-1133. Zbl0571.46006
  5. [5] W. Ruckle, FK spaces in which the sequence of coordinate functionals is bounded, Canad. J. Math. (1973), 973-978. Zbl0267.46008
  6. [6] W. Ruckle and S. Saxon, Generalized sectional convergence and multipliers, J. Math. Analysis and Appl. 193 (1995), 680-705. Zbl0881.46010
  7. [7] S. Saxon, Some normed barrelled spaces which are not Baire, Math. Ann. 209 (1974), 153-160. Zbl0295.46004
  8. [8] C. Stuart, Dense barrelled subspaces of Banach spaces, Collect. Math. 47 (1996), 137-143. Zbl0859.46004
  9. [9] C. Swartz, phIntroduction to Functional Analysis, Marcel Dekker, 1992. 

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