SciELO - Scientific Electronic Library Online

 
vol.29 número2COUNTABLE COMPACTNESS AND THE LINDELOF PROPERTY IN L-FUZZY TOPOLOGICAL SPACESEXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINE índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados

Articulo

Indicadores

Links relacionados

Compartir


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.29 n.2 Antofagasta ago. 2010

http://dx.doi.org/10.4067/S0716-09172010000200006 

Proyecciones Journal of Mathematics
Vol. 29, N° 2, pp. 137-144, August 2010.
Universidad Católica del Norte
Antofagasta - Chile


POINTWISE BOUNDEDNESS AND EQUICONTINUITY IN ß-DUALS


Charles Swartz

New Mexico State University, U. S. A.


Correspondencia a:


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

[1] [Bo] N. Bourbaki, Espaces Vectoriels Topologiques, Livre V, Herman, Paris, (1976).         [ Links ]

[2] [LPY] Lee Peng Yee, Sequence Spaces and the Gliding Hump Property, Southeast Asia Bull. Math., Special Issue, pp. 65-72, (1993).         [ Links ]

[3] [LS] Li Ronglu and C. Swartz, Spaces forWhich the Uniform Boundedness Principle Holds, Studia Sci. Math. Hung., 27, pp. 379-384, (1992).         [ Links ]

[4] [Ro] S. Rolewicz, Metric Linear Spaces, Polish Sci. Publ., Warsaw, (1972).         [ Links ]

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

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

[7] [Sw2] C. Swartz, A Multiplier Gliding Hump Property for Sequence Spaces, Proy. Revista de Mat., 20, pp. 20-32, (2001).         [ Links ]

[8] [Sw3] C. Swartz, Uniform Boundedness in Vector-Valued Sequence Spaces, Proy. J. Math., 23, pp. 236-240, (2004).         [ Links ]

[9] [Sw4] C. Swartz, Orlicz-Pettis Theorems for Multiplier Convergent Operator-Valued Series, Proy. J. Math., 23, pp. 61-72, (2004).         [ Links ]

[10] [Sw5] C. Swartz, Uniform Convergence of Multiplier Convergent Series, Proy. J. Math., 26, pp. 27-35, (2007).         [ Links ]

[11] [Sw6] C. Swartz, Multiplier Convergent Series, World Sci. Publ., Singapore, (2009).         [ Links ]

[12] [Sw7] C. Swartz, Boundedness and Uniform Convergence in ß-Duals, Proy. J. Math., 29, pp. 77-84, (2010).         [ Links ]

[13] [Wi] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, NY, (1978).         [ Links ]


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


Received : June 2010. Accepted : July 2010

Creative Commons License Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons