A forma fraca do teorema de peano em espaços de banach de dimensão infinita

Abstract

For a long time one was looking for an answer of Peano’s theorem in infinitedimensional Banach spaces. In 1974, Godunov proved that the Peano’s theorem holds in a Banach space X if and only if X has finite dimension. In the following, he turned all his attention to the weak form of Peano’s theorem in the infinite-dimensional case. In 2003, Shkarin proved that if X is a Banach space containing a complemented subspace with an unconditional Schauder basis, then the weak form of Peano’s theorem does not hold. In this work we try to show all details of the proof.