The Banach-Mazur distance between C(Δ) and C_0(Δ) equals 2
DOI:
https://doi.org/10.12775/TMNA.2023.025Keywords
Banach-Mazur distance, Cantor set, space of continuous functionsAbstract
Let $C(\Delta)$ denote the Banach space of all continuous real-valued functions on the Cantor set $\Delta$ and $C_0(\Delta)=\lbrace f\in C(\Delta): f(1)=0\rbrace$. From the 1966 theorem of Cambern, it is well-known that the Banach-Mazur distance $d(C(\Delta), C_0(\Delta))\geq 2$. We prove that, in fact, $d(C(\Delta), C_0(\Delta))= 2$. As a consequence, we answer a question left open in the 2012 paper of Candido and Galego.References
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Copyright (c) 2024 Łukasz Piasecki, Jeimer Villada
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