Complemented subspaces of homogeneous polynomials

Abstract

Let 𝐾(𝑛𝐸;𝐹) (resp. 𝑤(𝑛𝐸;𝐹)) denote the subspace of all 𝑃∈(𝑛𝐸;𝐹) which are compact (resp. weakly continuous on bounded sets). We show that if 𝐾(𝑛𝐸;𝐹) contains an isomorphic copy of 𝑐0, then 𝐾(𝑛𝐸;𝐹) is not complemented in (𝑛𝐸;𝐹). Likewise we show that if 𝑤(𝑛𝐸;𝐹) contains an isomorphic copy of 𝑐0, then 𝑤(𝑛𝐸;𝐹) is not complemented in (𝑛𝐸;𝐹).

Sergio A. Pérez

Instructor