Phelps Property U and $C(K)$ spaces
Ch. Cobollo, A. J. Guirao, V. Montesinos

TL;DR
This paper systematically studies Property U in Banach spaces, focusing on U-embeddings into $C(K)$ spaces, and explores conditions for their existence in various settings.
Contribution
It introduces the concept of U-embeddings and develops a framework for their analysis, especially into $C(K)$ spaces, extending prior understanding of Property U.
Findings
Established criteria for U-embeddings into $C(K)$ spaces.
Analyzed U-embeddings for finite-dimensional spaces.
Provided results for general Banach spaces.
Abstract
A subspace of a Banach space has whenever every continuous linear functional on has a unique norm-preserving (i.e., HahnBanach) extension to (Phelps, 1960). Throughout this document we introduce and develop a systematic study of the existence of between Banach spaces and , that is, isometric embeddings of into whose ranges have property U. In particular, we are interested in the case that , where is a compact Hausdorff topological space. We provide results for general Banach spaces and for some specific set-ups, such as being a finite-dimensional space or a -space.
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Topics in Algebra · Advanced Topology and Set Theory
