Nonseparable MLP versus LP

Determine whether every non-separable C*-algebra with the maximal lifting property also has the lifting property.

Background

The paper proves that, for separable C*-algebras, the maximal lifting property (MLP) is equivalent to the ordinary lifting property (LP), along with several other local and tensorial conditions. The authors explicitly leave unresolved whether this implication remains valid without separability.

References

It seems open whether a non-separable $C*$-algebra with MLP has the LP.

— Operator space theory from the maximal viewpoint  (2610.21929 - Pisier et al., 15 Oct 2026) in Section 5, Remark immediately following the proof of Theorem \ref{d6}