Bounded approximation property for Lipschitz-free spaces over uniformly discrete metric spaces

Determine whether every Lipschitz-free space over a uniformly discrete metric space has the bounded approximation property (BAP).

Background

The paper discusses structural properties of Lipschitz-free spaces over uniformly discrete (LFUD) metric spaces. Kalton observed several classical properties for LFUD spaces, and a longstanding problem concerns whether all such spaces enjoy the bounded approximation property. This problem is well-known in the field and carries significant consequences in Banach space theory.

References

One of the major open problems, originally posed by N. Kalton in p.~185, asks whether every LFUD space has the bounded approximation property (both positive and negative answer having interesting consequences, see Problem 18 for further discussion).

— Lipschitz-free spaces over uniformly discrete metric spaces are 3-Schur  (2604.01875 - Cúth et al., 2 Apr 2026) in Introduction (paragraph on LFUD spaces)