Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces
type: Item
instance of: scholarly article
title: Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces
zbMATH Open document ID: 0564.47009
author: Bernd Carl
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74689
review text: The paper deals with covering problems and the degree of compactness of operators. The main part is devoted to relationships between entropy moduli and Kolmogorov (resp. Gelfand and approximation) numbers for operators which may be interpreted as counterparts to the classical Bernstein-Jackson inequalities for functions. Certain quantifications of results in the Riesz-Schauder-Theory are given. Finally, the largest distance between ''the degree of approximation'' and the ''degree of compactness'' of integral operators in C[0,1] generated by smooth kernels is determined. For illustrating of the quantifications we treat some eigenvalue and compactness problems of nuclear operators and operators of Hille-Tamarkin-type.
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 3899602
zbMATH Keywords: covering problems
zbMATH Keywords: degree of compactness of operators
zbMATH Keywords: relationships between entropy moduli and Kolmogorov (resp. Gelfand and approximation) numbers
zbMATH Keywords: Bernstein-Jackson inequalities
zbMATH Keywords: Riesz-Schauder-Theory
zbMATH Keywords: degree of approximation
zbMATH Keywords: integral operators
zbMATH Keywords: smooth kernels
zbMATH Keywords: eigenvalue and compactness problems of nuclear operators
zbMATH Keywords: operators of Hille-Tamarkin- type
MaRDI profile type: Publication
OpenAlex ID: W1991581965
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DOI: 10.5802/AIF.1020
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 3899602