Relations between approximation numbers and entropy numbers
type: Item
instance of: scholarly article
title: Relations between approximation numbers and entropy numbers
zbMATH Open document ID: 0811.47020
published in: Journal of Approximation Theory
publication date: 1995-05-01T00:00:00Z
review text: Replacing in the definition of the norm the triangle inequality by the inequality \(\| u+v\|\leq c(\| u\|+ \| v\|)\), \(c\geq 1\) fixed, one obtains the notion of quasi-norm and the corresponding notion of quasi-Banach space. The aim of this paper is to study the interrelations between approximation numbers and entropy numbers of compact operators acting on quasi-Banach spaces. In the case of Banach spaces, similar results were obtained by B. Carl [see, e.g., \textit{B. Carl} and \textit{I. Stephani}, `Entropy compactness and the approximation of operators', Cambridge (1990; Zbl 0705.47017)]. Applications of general results to embedding operators between Besov-Hardy-Sobolev spaces are given.
Mathematics Subject Classification ID: 47B06
Mathematics Subject Classification ID: 46A16
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 636061
zbMATH Keywords: triangle inequality
zbMATH Keywords: quasi-Banach space
zbMATH Keywords: approximation numbers
zbMATH Keywords: entropy numbers
zbMATH Keywords: compact operators acting on quasi-Banach spaces
zbMATH Keywords: Besov-Hardy- Sobolev spaces
author: Hans Triebel
reviewed by: Stefan Cobzaş
MaRDI profile type: Publication
full work available at URL: jath.1994.1064
OpenAlex ID: W1976893022
DOI: 10.1006/JATH.1994.1064
description: scientific article; zbMATH DE number 636061