Boundedness and uniform convergence in B-duals.
DOI:
https://doi.org/10.4067/S0716-09172010000100008Keywords:
Vector sequence spaces, convergence, linear operators, espacios secuenciales vectoriales, convergencia, operadores lineales.Abstract
Suppose E is a vector valued sequence space with operator valued ß-dual EßY . If the space E satisfies certain gliding hump conditions, we consider the connection between pointwise bounded subsets A of EßY and the uniform convergence of the elements of A. For linear operators our results contain results of Li, Wang and Zhong for the spaces c0(X) and lp(X).References
Khaleelulla, S. M., Counterexamples in Topological Vector Spaces, Springer-Verlag, Heidelberg, (1982).
Li, R., Wang, F., Zhong, S., The strongest intrinsic meaning of sequential-evaluation convergence, Topology and its Appl., 154, pp. 1195-1205, (2007).
Stuart, C., Swartz, C., Uniform Convergence in the Dual of a Vector Valued Sequence Space, Taiwnese J. Math., 7, pp. 665-676, (2003).
Swartz, C., Infinite Matrices and the Gliding Hump, World Sci. Publ., (1996).
Swartz, C.,Orlicz-Pettis Theorems for Multiplier Convergent Operator Valued Series, Proy. J. Math., 23, pp. 61-72, (2004).
Swartz, C., Multiplier Convergent Series, World Sci. Publ., Singapore, 2009).
Swartz, C., An Abstract Gliding Hump Property, Proy.J. Math., 28, pp. 89-109, (2009).
Zhong, S., Li, R., Yang, H., Summability Results for Matrices of Quasi-homogeneous Operators, Proy. J. Math., 27, pp. 249-258, (2008)
Li, R., Wang, F., Zhong, S., The strongest intrinsic meaning of sequential-evaluation convergence, Topology and its Appl., 154, pp. 1195-1205, (2007).
Stuart, C., Swartz, C., Uniform Convergence in the Dual of a Vector Valued Sequence Space, Taiwnese J. Math., 7, pp. 665-676, (2003).
Swartz, C., Infinite Matrices and the Gliding Hump, World Sci. Publ., (1996).
Swartz, C.,Orlicz-Pettis Theorems for Multiplier Convergent Operator Valued Series, Proy. J. Math., 23, pp. 61-72, (2004).
Swartz, C., Multiplier Convergent Series, World Sci. Publ., Singapore, 2009).
Swartz, C., An Abstract Gliding Hump Property, Proy.J. Math., 28, pp. 89-109, (2009).
Zhong, S., Li, R., Yang, H., Summability Results for Matrices of Quasi-homogeneous Operators, Proy. J. Math., 27, pp. 249-258, (2008)
Published
2011-01-06
How to Cite
[1]
C. Swartz, “Boundedness and uniform convergence in B-duals.”, Proyecciones (Antofagasta, On line), vol. 29, no. 1, pp. 75-82, Jan. 2011.
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