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  • Author or Editor: A. Aizpuru x
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In this paper we study the Orlicz-Pettis property for a Boolean algebra. We characterize the countable Boolean algebras with this property and extend that study to some families of P(N). As a consequence, we obtain characterizations of weakly summing families in terms of the space c0 and in terms of some separation properties.

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Abstract  

We prove that some results on uniform convergence of sequences of unconditionally convergent series, in Banach spaces, can be generalized to sequences of weakly unconditionally Cauchy series.

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Abstract  

We prove a version of the Orlicz-Pettìs theorem within the frame of the Statistical Cesàro summability.

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Here we present a new proof of Blatter's result: a normed space is complete if every bounded closed convex subset has an element of minimum norm. We also present geometrical conditions for the existence of minimum-norm elements in bounded closed convex sets. Also, we characterize reflexivity in the class of Banach spaces by means of contraction functions. Furthermore, we study what happens if we remove the completeness hypothesis.

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