Description

• Title:
  The Banach-Mazur distance between C(Δ) and C_0(Δ) equals 2
• Creator:
  Piasecki, Łukasz;
  Villada, Jeimer
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 Łukasz Piasecki, Jeimer Villada;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2024.03.03
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 63, No 1 (March 2024); 227 - 232;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/49147/37876 ;https://apcz.umk.pl/TMNA/article/view/49147/37877
• Subject:
  Banach-Mazur distance, Cantor set, space of continuous functions;
  46A22, 46B03, 46B25 , 46E15
• Identifier: https://apcz.umk.pl/TMNA/article/view/49147
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other