Universal *-regularity for discrete amenable groups

Determine whether every discrete amenable group G is *- regular; that is, establish that for each closed two-sided ideal I ⊂ C*(G), I coincides with the closure of I ∩ L1(G) in the C*(G)-norm.

Background

The authors highlight long-standing uncertainty around -regularity in the discrete amenable setting. The question strengthens inquiries about C-uniqueness and asks for full -regularity, a property with deep connections to harmonic analysis and the ideal structure of group C-algebras.