Uniform convergence of multiplier convergent series

Authors

  • Charles Swartz New Mexico State University.

DOI:

https://doi.org/10.4067/S0716-09172007000100002

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 sumatoria.JPG 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 sumatoria.JPG 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.

Author Biography

Charles Swartz, New Mexico State University.

Mathematics Department. 

References

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Published

2017-04-18

How to Cite

[1]
C. Swartz, “Uniform convergence of multiplier convergent series”, Proyecciones (Antofagasta, On line), vol. 26, no. 1, pp. 27-35, Apr. 2017.

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