Strongly Bounded Partial Sums

Charles Swartz

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.

Palabras clave


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

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172014000200006

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