Inequalities between entropy and approximation numbers of compact maps
type: Item
instance of: scholarly article
title: Inequalities between entropy and approximation numbers of compact maps
zbMATH Open document ID: 0654.47008
DOI: 10.4171/ZAA/299
author: R. M. Edmunds
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1988-01-01T00:00:00Z
review text: Let H be a Hilbert space, T a compact operator on H having infinite dimensional range, \(a_ n(T)\) the nth approximation number of T, and \(e_ n(T)\) the nth entropy number. It is shown that if N is any positive integer then \[ e_ n(T)\leq 2a_{N+1}(T)\leq 2\sqrt{2}e_{N+2}(T) \] for any integer n for which \[ (n-1)\log 2\geq 2 \log \prod^{N}_{j=1}3a_ j(T)/a_{N+1}(T). \] From these inequalities the author derives others of a similar nature in which bounds for the approximation numbers give corresponding bounds for the entropy numbers.
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 4067657
zbMATH Keywords: approximation number
zbMATH Keywords: entropy number
reviewed by: James R. Holub
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4067657