Extension Property and Complementation of Isometric Copies of Continuous Functions Spaces

Autor(es)

Correa, Claudia ^[1] ; Tausk, Daniel V. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Matemat, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Results in Mathematics; v. 67, n. 3-4, p. 445-455, JUN 2015.
• Citações Web of Science: 2

Resumo

We prove that every isometric copy of C(L) in C(K) is complemented if L is a compact Hausdorff space of finite height and K is a compact Hausdorff space satisfying the extension property, i.e., every closed subset of K admits an extension operator. The space C(L) can be replaced by its subspace C(L vertical bar F) consisting of functions that vanish on a closed subset F of L. We also study the class of spaces having the extension property, establishing some stability results for this class and relating it to other classes of compact spaces. (AU)

• Processo FAPESP: 12/25171-0 - Estudo de problemas em espaços de Banach da forma C(K)
• Beneficiário: Claudia Correa de Andrade Oliveira
• Modalidade de apoio: Bolsas no Brasil - Doutorado