2019/09/16 by Antunes, Leandro, Beanland, Kevin, Braga, Bruno de Mendonça
#FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)
paper · doi:10.48550/arxiv.1909.07475
This paper deals with the problem of when, given a collection \mathcal C of weakly compact operators between separable Banach spaces, there exists a separable reflexive Banach space Z with a Schauder basis so that every element in \mathcal C factors through Z (or through a subspace of Z). A sample result is the existence of a reflexive space Z with a Schauder basis so that for each separable Banach space X, each weakly compact operator from X to L1 factors through Z. We also prove the following descriptive set theoretical result: Let \mathcal L be the standard Borel space of bounded operators between separable Banach spaces. We show that if \mathcal B is a Borel subset of weakly compact operators between Banach spaces with separable duals, then the assignment A∈ \mathcal B→ A^* can be realized by a Borel map \mathcal B→ \mathcal L.