The structure of free Banach spaces and of their second duals
Program
Standard projects
Provider
Czech Science Foundation
Departments
Investigators
Code
GA22-32829S
Period
2022 - 2024
Description
Free Banach spaces play an important role in the study of nonlinear geometry of Banach
spaces and in areas involving transportation problems. This brings them to the forefront of
modern functional analysis and interest in them continues to grow. The free space of a metric space M is given by the fact that M isometrically embeds in it and that any Lipschitz map from M to a Banach space extends uniquely to a bounded linear map from the free space. This allows the linearization of nonlinear problems, but at the cost of a complicated linear structure. Its closer examination is the aim of our project. The free space lies in the dual of the space of Lipschitz functions and forms its predual. Hence, one should analyze all three of the spaces to understand free space. We intend to study representation of functionals on the spaces of Lipschitz functions and topological aspects of isomorphic free spaces. This could contribute to solving some known open problems in the area, such as the complementability in the bidual, predual uniqueness, or the existence of isomorphisms of certain free spaces.