Jung constants of the \(\ell ^ n_ p\)-spaces
type: Item
instance of: scholarly article
title: Jung constants of the \(\ell ^ n_ p\)-spaces
zbMATH Open document ID: 0727.46005
DOI: 10.1007/BF01139599
published in: Mathematical Notes
publication date: 1990-01-01T00:00:00Z
review text: Let \(B_ 2\) be a subspace of a normed space \(B_ 1\), and let \(M\subset B_ 2\). Defne the Chebyshev radius \(r_{B_ 1}(M):=\inf_{x\in B_ 1}\sup_{y\in M}\| x-y\|_{B_ 2},\) and let \(d_{B_ 2}(M_ 2)\) be the diameter of M in \(B_ 2\). Define the Jung constant \(I(B_ 1,B_ 2)=\sup \{r_{B_ 1}(M)/d_{B_ 2}(M):\) \(M\subset B_ 2\}.\) In the paper there are given upper and lower estimates of Jung constants for finite dimensional spaces with mixed \(\ell_ p\)-norms in terms of the norm of a certain interpolation operator, and with a precise dependence on the dimension. This, in particular, yields an exact evaluation of Jung constants for infinite dimensional \(L_ p\)-spaces with an atomless measure.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46B07
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 4200916
zbMATH Keywords: Chebyshev radius
zbMATH Keywords: upper and lower estimates of Jung constants for finite dimensional spaces with mixed \(\ell _ p\)-norms in terms of the norm of a certain interpolation operator
zbMATH Keywords: exact evaluation of Jung constants for infinite dimensional \(L_ p\)-spaces with an atomless measure
author: Valeriĭ I. Ivanov
author: S. A. Pichugov
reviewed by: Jerzy Szulga
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4200916