A projection property and weak sequential completeness of alfa-duals

• Autores: Charles Swartz, Christopher E. Stuart
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 43, Fasc. 2, 1992, págs. 177-185
• Idioma: inglés
• Títulos paralelos:
  • Una propiedad de proyección y completitud secuencial débil de espacios alfa-duales
• Enlaces
  • Texto completo
• Resumen

  • In [7] the Hahn-Schur Theorem from summability was used to give a simple proof of a result of Bennett on the weak sequential completeness of the $\alpha$-dual of a monotone sequence space ([2]). In this note we point out that the same method of proof employed in [7] can be used to give a generalization of Bennett’s result to a wider class of sequence spaces than the monotone spaces. As was the case in [7], the methods are also applicable to vector-valued sequence spaces.

• Referencias bibliográficas
  • P. Antosik and C. Swartz, Matrix Methods in Analysis, Lecture Notes in Math. 1113 (1985), Springer-Verlag, Heidelberg.
  • G. Bennett, A new class of sequence spaces with applications in summability theory, J. Reine Angew. Math. 266 (1974), 49–75.
  • R. Haydon, A non-reflexive Grothendieck space that does not contain $\ell^\infty$, Israel J. of Math. 40 (1981), 65–73.
  • I. Maddox, Infinite Matrices of Operators, Lecture Notes in Math. 786 (1980), Springer-Verlag, Berlin.
  • D. Noll, Sequential completeness and spaces with the gliding humps property, Manuscripta Math. 66 (1990), 237–252.
  • R. Samaraunga and J. Sember, Summability and substructures of $2^N$, Southeast Asia Math. Bull. 12 (1988), 11–22.
  • C. Swartz, Weak Sequential Completeness of Sequence Spaces, Collect. Math. 43, 1 (1992), 55–61.
  • C. Swartz, An Introduction to Functional Analysis, Marcel Dekker, 1992.