Strong topologies for multiplier convergent series

Authors

  • Charles Swartz New Mexico State University.

DOI:

https://doi.org/10.4067/S0716-09172006000200001

Keywords:

Normed linear spaces, Orlicz-Pettis Theorem, convergent series, locally convex topology, weak topology, espacios lineales normados, teorema de Orlicz-Pettis, series convergentes, topología localmente convergente, topología débil.

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.

Author Biography

Charles Swartz, New Mexico State University.

Department of Mathematical Sciences.

References

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Published

2017-05-08

How to Cite

[1]
C. Swartz, “Strong topologies for multiplier convergent series”, Proyecciones (Antofagasta, On line), vol. 25, no. 2, pp. 111-120, May 2017.

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Section

Artículos