Complemented subspaces of homogeneous polynomials

2016/12/06 by Sergio Andrés Pérez León, León, Sergio Andrés Pérez · 1 citation
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Holomorphic and Operator Theory #math.FA

paper · pdf · doi:10.48550/arxiv.1612.01742

8 pages

arxiv created 2016/12/06 · openalex publication_date 2016/12/06 · arxiv updated 2016/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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• Complemented subspaces of polynomial ideals

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