Pointwise Boundedness and Equicontinuity in β-Duals.

• Swartz, Charles ^[1]
  1. [1] New Mexico State University

     New Mexico State University

     Estados Unidos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 29, Nº. 2, 2010, págs. 137-144
• Idioma: inglés
• DOI: 10.4067/S0716-09172010000200006
• Enlaces
  • Texto completo
• Resumen

  • Let E be a vector valued sequence space with operator valued ß- dual EßY. If E satisfies certain gliding hump assumptions, we show that pointwise bounded subsets of EßY are sequentially equicontinuous. The result is established by considering uniform convergence of the elements in EßY

• Referencias bibliográficas
  • Citas N. Bourbaki, Espaces Vectoriels Topologiques, Livre V, Herman, Paris, (1976).
  • Lee Peng Yee, Sequence Spaces and the Gliding Hump Property, Southeast Asia Bull. Math., Special Issue, pp. 65-72, (1993).
  • Li Ronglu and C. Swartz, Spaces for Which the Uniform Boundedness Principle Holds, Studia Sci. Math. Hung., 27, pp. 379-384, (1992).
  • S. Rolewicz, Metric Linear Spaces, Polish Sci. Publ., Warsaw, (1972).
  • C. Stuart and C. Swartz, Uniform Convergence in the Dual of a Vector-Valued Sequence Space, Taiwan. J. Math., 7, pp. 665-676, (2003).
  • C. Swartz, Infinite Matrices and the Gliding Hump, World Sci. Publ. Singapore, (1996).
  • C. Swartz, A Multiplier Gliding Hump Property for Sequence Spaces, Proy. Revista de Mat., 20, pp. 20-32, (2001).
  • C. Swartz, Uniform Boundedness in Vector-Valued Sequence Spaces, Proy. J. Math., 23, pp. 236-240, (2004).
  • C. Swartz, Orlicz-Pettis Theorems for Multiplier Convergent Operator-Valued Series, Proy. J. Math., 23, pp. 61-72, (2004).
  • C. Swartz, Uniform Convergence of Multiplier Convergent Series, Proy. J. Math., 26, pp. 27-35, (2007).
  • C. Swartz, Multiplier Convergent Series, World Sci. Publ., Singapore (2009).
  • C. Swartz, Boundedness and Uniform Convergence in β-Duals, Proy. J. Math., 29, pp. 77-84, (2010).
  • A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, NY, (1978).