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On surjections between Banach spaces of continuous functions on separable nonmetrizable compact lines

Volume 246 / 2019

Artur Michalak Fundamenta Mathematicae 246 (2019), 301-320 MSC: Primary 46E15, 46B03, 54F05. DOI: 10.4064/fm600-9-2018 Published online: 15 April 2019

Abstract

For a compact subset $K$ of $[0,1]$ and a subset $A$ of $K$, we denote by $K_A$ the modification of the two-arrows space with base $K$ and duplicated set $A$. We study necessary conditions for the existence of continuous linear surjections between the Banach spaces $C(K_A)$ of all real continuous functions on $K_A$ spaces. We show that if there exists a continuous linear surjection from $C(K_A)$ onto $C(L_B)$ and $A$ is a member of the additive Borel class $\Sigma _\alpha $ for some ordinal number $1\leq \alpha \leq \omega _1$, then $B\in \Sigma _{\max\{3,1+\alpha \}}$.

Authors

  • Artur MichalakFaculty of Mathematics and Computer Science
    A. Mickiewicz University, Poznań
    Umultowska 87
    61-614 Poznań, Poland
    e-mail

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