Equivalence of Fraïssé and weak Fraïssé properties

Determine whether every weak Fraïssé Banach space is Fraïssé; equivalently, establish whether the classes of Fraïssé and weak Fraïssé Banach spaces coincide.

Background

Weak Fraïssé and Fraïssé properties capture approximate ultrahomogeneity with differing uniformity in the approximation parameters. Many structural consequences are known for Fraïssé spaces (e.g., oligomorphy), but it is unknown whether the additional uniformity required in the Fraïssé definition yields a strictly smaller class than weak Fraïssé.

Settling this question would sharpen the hierarchy of approximate homogeneity notions in Banach space theory.

References

It is not knwon whether the classes of Fraïssé and weak Fraïssé Banach spaces coincide.

— Isometric rigidity and Fraïssé properties of Orlicz sequence spaces  (2604.02080 - Rancourt et al., 2 Apr 2026) in Section 1.1 (Fraïssé theory for Banach spaces)