2022/10/18 by Cobollo, Ch., Guirao, A. J., Montesinos, V.
#46B04 (Primary) 46A22 #46B20 #46E15 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2210.10178
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, 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 are interested in the case that Y=C(K), where K is a compact Hausdorff topological space. We provide results for general Banach spaces and for some specific set-ups, such as X being a finite-dimensional space or a C(K)-space.