Estelle Basset (LmB) : The Point of Continuity Property in some Lipschitz-free spaces
Abstract: The Point of Continuity Property (PCP) is a property that characterizes whether the weak topology and the norm topology agree at some points on the subspaces of a Banach space. We will introduce Lipschitz-free spaces, which are specific Banach spaces in which the PCP is expressed in a simpler way. After defining an index named « weak-fragmentability index » which measures « at which point » a Banach space has the PCP, we will see that there exist Lipschitz-free spaces with arbitrarly high weak-fragmentability index, and what are the consequences of this result.