Dense barrelled subspace of Banach spaces

• Autores: Christopher E. Stuart
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 47, Fasc. 2, 1996, págs. 137-143
• Idioma: inglés
• Enlaces
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• Resumen

  • In this note, we give a gliding hump characterization of the dense barrelled solid subspaces of $\ell^1$ (recall that a sequence is solid if $\ell^\infty\cdot E=E$). Also, we present a sufficient condition for a dense subspace of $\ell^1$ to be barrelled, without assuming solidness, and generalizations to dense subspaces of arbitrary Banach spaces.

• Referencias bibliográficas
  • G. Bennett, A new class of sequence spaces with applications in summability theory, J. Reine Angew. Math. 266 (1974), 49–75.
  • G. Bennett, Some inclusion theorems for sequence spaces, Pacific J. Math. 64(1) (1973), 17–30.
  • W. Ruckle, The strong $\phi$ topology on symmetric sequence spaces, Canad. J. Math. 37 (1985), 1112–1133.
  • W. Ruckle and S. Saxon, Generalized sectional convergence and multipliers, preprint.
  • S. Saxon, Some normed barrelled subspaces which are not Baire, Math. Ann. 209 (1974), 153–160.
  • S. Saxon, Non-barrelled dense $\beta\phi$ subspaces, preprint.
  • A. Wilansky, Modern Methods in Topological Vector Spaces, New York, McGraw-Hill, 1978.