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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.25 n.2 Antofagasta ago. 2006

http://dx.doi.org/10.4067/S0716-09172006000200001 

Proyecciones Journal of Mathematics
Vol. 25, No 2, pp. 111-120, August 2006.
Universidad Católica del Norte
Antofagasta - Chile

STRONG TOPOLOGIES FOR MULTIPLIER CONVERGENT SERIES

CHARLES SWARTZ

NEW MEXICO STATE UNIVERSITY, U.S.A.


Abstract

P. Dierolf has shown that there is a strongest locally convex polar topology which has the same subseries (bounded multiplier) convergent series as the weak topology, and I. Tweddle has shown that there is a strongest locally convex topology which has the same subseries convergent series as the weak topology. We establish the analogues of these results for multiplier convergent series if the sequence space of multipliers has the signed weak gliding hump property. We compare our main result with other known Orlicz-Pettis Theorems for multiplier convergent series.


 

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Received : December 2005. Accepted : June 2006

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