Proyecciones Journal of Mathematics
Vol. 29, N° 1, pp. 75-82, May 2010.
Universidad Católica del Norte
Antofagasta - Chile


BOUNDEDNESS AND UNIFORM CONVERGENCE IN B-DUALS


Charles Swartz

New Mexico State University, U.S.A.


Correspondencia a:

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

[Kh] Khaleelulla, S. M., Counterexamples in Topological Vector Spaces, Springer-Verlag, Heidelberg, (1982).        [ Links ]

[LWZ] Li, R., Wang, F., Zhong, S., The strongest intrinsic meaning of sequential-evaluation convergence, Topology and its Appl., 154, pp. 1195-1205, (2007).        [ Links ]

[SS] Stuart, C., Swartz, C., Uniform Convergence in the Dual of a Vector- Valued Sequence Space, Taiwnese J. Math., 7, pp. 665-676, (2003).        [ Links ]

[Sw1] Swartz, C., Infinite Matrices and the Gliding Hump, World Sci. Publ., (1996).        [ Links ]

[Sw2] Swartz, C.,Orlicz-Pettis Theorems for Multiplier Convergent Operator Valued Series, Proy. J. Math., 23, pp. 61-72, (2004).        [ Links ]

[Sw3] Swartz, C., Multiplier Convergent Series, World Sci. Publ., Singapore, (2009).        [ Links ]

[Sw4] Swartz, C., An Abstract Gliding Hump Property, Proy.J. Math., 28, pp. 89-109, (2009).        [ Links ]

[ZLW] Zhong, S., Li, R., Yang, H., Summability Results for Matrices of Quasi-homogeneous Operators, Proy. J. Math., 27, pp. 249-258, (2008).        [ Links ]

Received : November 2009. Accepted : December 2010

Charles Swartz
Mathematics Department
New Mexico State University
Las Cruces
NM 88003
U. S. A.
e-mail : cswartz@nmsu.edu