Pointwise Boundedness and Equicontinuity in ß-Duals.
DOI:
https://doi.org/10.4067/S0716-09172010000200006Keywords:
Vector spaces, operators, espacios vectoriales, operadores.Abstract
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.References
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).
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).
Published
2011-01-07
How to Cite
[1]
C. Swartz, “Pointwise Boundedness and Equicontinuity in ß-Duals.”, Proyecciones (Antofagasta, On line), vol. 29, no. 2, pp. 137-144, Jan. 2011.
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