Description

• Title:
  Retracting a ball in ℓ_1 onto its simple spherical cap
• Creator:
  Intrakul, Jumpot;
  Iampiboonvatana, Smith Yokpaisan
• Description:
  In this article, a notion and classification of spherical caps in the sequence space $\ell_1$ are introduced, and the least Lipschitz constant of Lipschitz retractions from the unit ball onto a spherical cap is defined. In addition, an approximation of this value for the specific spherical cap, the simple spherical cap, is calculated. This approximation reveals a rough relation between these values, denoted by $\kappa(\alpha)$, and the answer of the optimal retraction problem for the space $\ell_1$, denoted by $k_0(\ell_1)$. To be precise, there exists $-1< \mu< 0$ such that $k_0(\ell_1)\leq\kappa(\alpha)\leq2+k_0(\ell_1)$ whenever $-1< \alpha< \mu$; here $\alpha$ is the level of spherical cap.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 Jumpot Intrakul, Smith Yokpaisan Iampiboonvatana;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2024.03.19
• 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); 115 - 129;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/49535/38064 ;https://apcz.umk.pl/TMNA/article/view/49535/38065
• Subject:
  Lipschitzian;
  optimal retraction;
  sequence space;
  spherical cup;
  Primary: 47H09, 47H99;
  Secondary: 54C15
• Identifier: https://apcz.umk.pl/TMNA/article/view/49535
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other