Strong topologies for multiplier convergent series

• 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. 25, Nº. 2, 2006, págs. 111-120
• Idioma: inglés
• DOI: 10.4067/S0716-09172006000200001
• Enlaces
  • Texto completo
• Resumen

  • P. Dierolf has shown that there is a strongest locally convex polar topology which has the same subseries (bounded multiplier) convergent series as the weak topology, and I. Tweddle has shown that there is a strongest locally convex topology which has the same subseries convergent series as the weak topology. We establish the analogues of these results for multiplier convergent series if the sequence space of multipliers has the signed weak gliding hump property. We compare our main result with other known Orlicz-Pettis Theorems for multiplier convergent series.

• Referencias bibliográficas
  • Citas [1] G. Bennett and N. Kalton, FK Spaces containing c0, Duke Math. J.,39(1972),561-582.
  • [2] J. Boos, C. Stuart and C. Swartz,Gliding Hump Properties for Matrix Domains, Analysis Mathematica, 30, pp. 243-257, (2004).
  • [3] P. Dierolf, Theorems of Orlicz-Pettis type for locally convex spaces, Man. Math., 20, pp. 73-94, (1977).
  • [4] N. Dinculeanu, Weak compactness and uniform convergence of operators in spaces of Bochner integrable functions, J. Math. Anal. Appl.,...
  • [5] G. Kothe, Topological Vector Spaces I, Springer-Verlag, NY, (1983).
  • [6] Li Ronglu, Cui Chengri and Mingyung Cho, Invariants on all admissible polar topologies, Chinese Annals of Math., 19, pp. 1-6, (1998).
  • [7] C. McArthur, On a Theorem of Orlicz-Pettis, Pacific J. Math., 22, pp. 297-302, (1967).
  • [8] W. Orlicz, Bietrage zur Theorie Orthogonalent Wicklungen III, Studia Math., 1, pp. 241-255, (1929).
  • [9] B. J. Pettis, Integration in Vector Spaces, Trans. Amer. Math. Soc., 44, pp. 277-304, (1938).
  • [10] C. Stuart, Weak Sequential Completeness in Sequence Spaces, Ph.D. Dissertation, New Mexico State University, (1993).
  • [11] C. Stuart, Weak Sequential Completeness of β-Duals, Rocky Mountain Math. J., 26, pp. 1559-1568, (1996).
  • [12] C. Stuart and C. Swartz, Orlicz-Pettis Theorems for Multiplier Convergent Series, Journal for Analysis and Appl., 17, pp. 805-811, (1998).
  • [13] C. Stuart and C. Swartz, Generalizations of the Orlicz-Pettis Theorem,
  • [14] C. Swartz, An Introduction to Functional Analysis, Marcel Dekker, NY, (1992)
  • [15] C. Swartz, Infinite Matrices and the Gliding Hump, World Sci. Publ.,Singapore, (1996).
  • [16] C. Swartz, Orlicz-Pettis Theorems for Multiplier Convergent Operator Valued Series, Proy. J. Math., 23, pp. 61-72, (2004).
  • [17] I. Tweddle, Vector-Valued Measures, Proc. London Math. Soc., 20, pp. 469-489, (1970).
  • [18] A. Wilansky, Modern Methods in Topological Vector Spaces, McGrawHill, NY, (1978).
  • [19] Wu Junde and Li Ronglu, Basic Properties of locally convex A-Spaces, Studia Sci. Math., 35, pp. 353-358, (1999).