Description

• Title:
  Convex hull deviation and contractibility
• Creator:
  Ivanov, Grigory M.
• Description:
  We study the Hausdorff distance between a set and its convex hull. Let $X$ be a Banach space, define the CHD-constant of the space $X$ as the supremum of this distance over all subsets of the unit ball in $X$. In the case of finite dimensional Banach spaces we obtain the exact upper bound of the CHD-constant depending on the dimension of the space. We give an upper bound for the CHD-constant in $L_p$ spaces. We prove that the CHD-constant is not greater than the maximum of Lipschitz constants of metric projection operators onto hyperplanes. This implies that for a Hilbert space the CHD-constant equals $1$. We prove a characterization of Hilbert spaces and study the contractibility of proximally smooth sets in a uniformly convex and uniformly smooth Banach space.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Date:
  2017.07.07
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 50, No 1 (September 2017); 9 - 25;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.089/12382 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.089/12383
• Subject:
  Hausdorff distance;
  characterization of inner product spaces;
  contractibility of a union of balls;
  52A07;
  52A27;
  52A35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.089
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other