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

Erik BalderMaria GirardiVincent Jalby — 1994

Studia Mathematica

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

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