Strongly Bounded Partial Sums

  • Charles Swartz New Mexico State University.
Palabras clave: Orlicz-Pettis Theorem, locally convex spaces, convergence, teorema de Orlicz-Pettis, espacios localmente convexos, convergencia.

Resumen

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.

Biografía del autor/a

Charles Swartz, New Mexico State University.
Department of Mathematics.

Citas

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Publicado
2017-03-23
Cómo citar
Swartz, C. (2017). Strongly Bounded Partial Sums. Proyecciones. Journal of Mathematics, 33(2), 205-213. https://doi.org/10.4067/S0716-09172014000200006
Sección
Artículos