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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

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SWARTZ, CHARLES. UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES. Proyecciones (Antofagasta) [online]. 2007, vol.26, n.1, pp. 27-35. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172007000100002.

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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