Some remarks on Phelps property U of a Banach space into C(K) spaces

A subspace X of a Banach space Y has Property U whenever every continuous linear functional on X has a unique norm-preserving (i.e., Hahn–Banach) extension to Y (Phelps in Trans Am Math Soc 95:238–255, 1960). Throughout this document, we introduce and develop a systematic study of the existence of U-embeddings between Banach spaces X and Y , that is, isometric embeddings of X into Y whose ranges have property U. In particular, we focus on the case Y = C ( K ) , where K is a compact Hausdorff topological space. We provide results for X a reflexive or another C ( K ) space.