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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.26 n.1 Antofagasta mayo 2007

http://dx.doi.org/10.4067/S0716-09172007000100002 

Proyecciones Journal of Mathematics
Vol. 26, No1, pp. 27-35, May 2007.
Universidad Católica del Norte
Antofagasta - Chile



UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES

CHARLES SWARTZ NEW MEXICO STATE UNIVERSITY

Correspondencia a:



Abstract

If λ is a sequence K-space and Σ xj is a series in a topological vector space X; the series is said to be λ-multiplier convergent if the series converges in X for every t = {tj} λ. We show that if λ satisfies a gliding hump condition, called the signed strong gliding hump condition, then the series converge uniformly for t = {tj} belonging to bounded subsets of λ. A similar uniform convergence result is established for a multiplier convergent series version of the Hahn-Schur Theorem.

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

Received : December 2006. Accepted : February 2007