Extension Property and Complementation of Isometric Copies of Continuous Functions Spaces

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• 作者：Claudia Correa ; Daniel V. Tausk
• 关键词：46B20 ; 46E15 ; 54G12 ; Banach spaces of continuous functions ; extension and averaging operators ; complementation of subspaces
• 刊名：Results in Mathematics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：67
• 期：3-4
• 页码：445-455
• 全文大小：486 KB
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• 作者单位：Claudia Correa (1)
  Daniel V. Tausk (1)
  
  1. Departamento de Matem谩tica, Universidade de S茫o Paulo, S茫o Paulo, Brazil
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-9012

文摘

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|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.