2020/10/19 by Sergio Andrés Pérez León, León, Sergio Andrés Pérez
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #Combinatorics #FOS: Mathematics #Functional Analysis (math.FA) #Geometry #Holomorphic and Operator Theory #Ideal (ethics) #Linear subspace #Mathematical analysis #Mathematics #Operator (biology) #Physics #Polynomial #math.FA
paper · pdf · doi:10.48550/arxiv.2010.10933
arXiv admin note: substantial text overlap with arXiv:1612.01742
arxiv created 2020/10/19 · openalex publication_date 2020/10/19 · arxiv updated 2020/10/22 · openalex created_date 2020/10/29 · openalex updated_date 2026/07/28
Given the polynomial ideal J\circP (nE; F), we prove that if J\circP (nE; F) contains an isomorphic copy of c0, then J\circP (nE; F) is not complemented in P (nE; F) for every closed operator ideal J⊂ LK and every n∈ℕ. Likewise we show that if \widehat(J\circL)fac(nE;F) contains an isomorphic copy of c0, then \widehat(J\circL)fac(nE;F) is not complemented in P(nE; F) for every closed operator ideal J⊂ LK and every n>1. When J=LK, these results generalizes results of several authors \citeLEW,\citeEM,\citeKALTON,\citeIOANA,\citeSERGIO, among others.