This is an announcement for the paper "Extension property and complementation of isometric copies of continuous functions spaces" by Claudia Correa and Daniel V. Tausk.

Abstract: In this article we prove that every isometric copy of C(L) in C(K) is complemented if L is compact Hausdorff 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. In particular, we obtain that every isometric copy of c_0(I) in C(K) is complemented, if K has the extension property. Finally, we study the class of spaces having the extension property, establishing some closure results for this class and relating it to other classes of compact spaces.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46E15, 54G12

Remarks: 9 pages

Submitted from: tausk@ime.usp.br

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1302.4661

or

http://arXiv.org/abs/1302.4661