The radii of sections of origin-symmetric convex bodies and their applications

Kushpel A., TAŞ K.

Journal of Complexity, vol.62, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 62
  • Publication Date: 2021
  • Doi Number: 10.1016/j.jco.2020.101504
  • Journal Name: Journal of Complexity
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Convex body, Multiplier, Volume, Width
  • Uşak University Affiliated: Yes

Abstract

Let V and W be any convex and origin-symmetric bodies in Rn . Assume that for some A ∈LRn→Rn, detA≠0, V is contained in the ellipsoid A−1B2n, where B2n is the unit Euclidean ball. We give a lower bound for the W-radius of sections of A−1V in terms of the spectral radius of A∗A and the expectations of ‖⋅‖V and ‖⋅‖Wo with respect to Haar measure on Sn−1⊂Rn. It is shown that the respective expectations are bounded as n→∞ in many important cases. As an application we offer a new method of evaluation of n-widths of multiplier operators. As an example we establish sharp orders of n-widths of multiplier operators Λ:LpMd→LqMd, 1