Strongly Bounded Partial Sums

• 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. 33, Nº. 2, 2014, págs. 205-213
• Idioma: inglés
• DOI: 10.4067/S0716-09172014000200006
• Enlaces
  • Texto completo
• Resumen

  • If λ is a scalar sequence space, a series P Zj in a topological vector space Z is λ multiplier convergent in Z if the series P ∞J =1 tj Zj converges in Z for every t = {tj} ∈ λ-If λ satisfies appropriate conditions, a series in a locally convex space X which is λ multiplier convergent in the weak topology is λ multiplier convergent in the original topology ofthe space (the Orlicz-Pettis Theorem) but may fail to be λ multiplier convergent in the strong topology of the space. However, we show under apprpriate conditions on the multiplier space λ that the series will have strongly bounded partial sums.

• Referencias bibliográficas
  • Citas [1] G. Bennett, A New Class of Sequence Spaces with Applications to Summability Theory, J. Reine Angew. Math., 266, pp. 49-75, (1974).
  • [2] J. Boos, Classical and Modern Methods in Summability, Oxford University Presss, Oxford, (2000).
  • [3] J. Boos, C. Stuart, C. Swartz, Gliding Hump Properties and Matrix Domains, Analysis Math., 30, pp. 243-257, (2004).
  • [4] P. K. Kamthan and M. Gupta, Sequence Spaces and Series, Marcel Dekker, N. Y., (1981).
  • [5] G. K¨ othe, Topological Vector Spaces I, Springer Verlag, Berlin, (1969).
  • [6] C. W. McArthur, On a Theorem of Orlicz and Pettis, Pacific J. Math., 22, pp. 297-303, (1967).
  • [7] D. Noll, Sequential Completeness and Spaces with the Gliding Humps Property, Manuscripta Math., 66, pp. 237-252, (1990).
  • [8] C. Stuart, Weak Sequential Completeness of β-Duals, Rocky Mountain Math. J., 26, pp. 1559-1568, (1996).
  • [9] C. Swartz, Multiplier Convergent Series, World Sci. Publ., Singapore, (2009).
  • [10] C. Swartz, An Abstract Gliding Hump Property, Proy.J. Math., 28, pp. 89-109, (2009).
  • [11] A. Wilansky, Modern Methods in Topological Vector Spaces, McGrawHill, N. Y., (1978).