Displaying similar documents to “Weak-star point of continuity property and Schauder bases”

An interplay between the weak form of Peano's theorem and structural aspects of Banach spaces

C. S. Barroso, M. A. M. Marrocos, M. P. Rebouças (2013)

Studia Mathematica

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We establish some results that concern the Cauchy-Peano problem in Banach spaces. We first prove that a Banach space contains a nontrivial separable quotient iff its dual admits a weak*-transfinite Schauder frame. We then use this to recover some previous results on quotient spaces. In particular, by applying a recent result of Hájek-Johanis, we find a new perspective for proving the failure of the weak form of Peano's theorem in general Banach spaces. Next, we study a kind of algebraic...