Displaying similar documents to “Vector series whose lacunary subseries converge”

Lacunary convergence of series in L revisited.

Lech Drewnowski (2000)

Revista Matemática Complutense

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A simpler proof is given for the recent result of I. Labuda and the author that a series in the space L (lambda) is subseries convergent if each of its lacunary subseries converges.

From weak to strong types of L E 1 -convergence by the Bocce criterion

Erik Balder, Maria Girardi, Vincent Jalby (1994)

Studia Mathematica

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Necessary and sufficient oscillation conditions are given for a weakly convergent sequence (resp. relatively weakly compact set) in the Bochner-Lebesgue space ℒ E 1 to be norm convergent (resp. relatively norm compact), thus extending the known results for ℒ ℝ 1 . Similarly, necessary and sufficient oscillation conditions are given to pass from weak to limited (and also to Pettis-norm) convergence in ℒ E 1 . It is shown that tightness is a necessary and sufficient condition to pass from limited to...

Topological Dichotomy and Unconditional Convergence

Lefevre, Pascal (1999)

Serdica Mathematical Journal

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In this paper, we give a criterion for unconditional convergence with respect to some summability methods, dealing with the topological size of the set of choices of sign providing convergence. We obtain similar results for boundedness. In particular, quasi-sure unconditional convergence implies unconditional convergence.