Strongly Bounded Partial Sums

Authors

  • Charles Swartz New Mexico State University.

DOI:

https://doi.org/10.4067/S0716-09172014000200006

Keywords:

Orlicz-Pettis Theorem, locally convex spaces, convergence, teorema de Orlicz-Pettis, espacios localmente convexos, convergencia.

Abstract

If λ is a scalar sequence space, a series P Zj in a topological vector space Z is λ multiplier convergent in Z if the series P ∞J =1 tj Zj converges in Z for every t = {tj} ∈ λ-If λ satisfies appropriate conditions, a series in a locally convex space X which is λ multiplier convergent in the weak topology is λ multiplier convergent in the original topology ofthe space (the Orlicz-Pettis Theorem) but may fail to be λ multiplier convergent in the strong topology of the space. However, we show under apprpriate conditions on the multiplier space λ that the series will have strongly bounded partial sums.

Author Biography

Charles Swartz, New Mexico State University.

Department of Mathematics.

References

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Published

2017-03-23

How to Cite

[1]
C. Swartz, “Strongly Bounded Partial Sums”, Proyecciones (Antofagasta, On line), vol. 33, no. 2, pp. 205-213, Mar. 2017.

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