Extension property and complementation of isometric copies of continuous\n functions spaces

2013/02/19 by Claudia Correa, Correa, Claudia, Daniel V. Tausk +1
Mathematics · #46B20 #46E15 #54G12 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1302.4661

openalex publication_date 2013/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we prove that every isometric copy of C(L) in C(K) is\ncomplemented if L is compact Hausdorff of finite height and K is a compact\nHausdorff space satisfying the extension property, i.e., every closed subset of\nK admits an extension operator. The space C(L) can be replaced by its subspace\nC(L|F) consisting of functions that vanish on a closed subset F of L. We also\nstudy the class of spaces having the extension property, establishing some\nclosure results for this class and relating it to other classes of compact\nspaces.\n

Related

• Extension of Operators from Weak^*-closed Subspaces of ℓ₁
• The complemented subspace problem for C(K)-spaces: A counterexample
• On embedding separable spaces C(L) in arbitrary spaces C(K)
• Extending continuous functions
• On the extension of Hölder maps with values in spaces of continuous functions