# Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces

Annales de l'institut Fourier (1985)

- Volume: 35, Issue: 3, page 79-118
- ISSN: 0373-0956

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topCarl, Bernd. "Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces." Annales de l'institut Fourier 35.3 (1985): 79-118. <http://eudml.org/doc/74689>.

@article{Carl1985,

abstract = {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.},

author = {Carl, Bernd},

journal = {Annales de l'institut Fourier},

keywords = {covering problems; degree of compactness of operators; relationships between entropy moduli and Kolmogorov (resp. Gelfand and approximation) numbers; Bernstein-Jackson inequalities; Riesz-Schauder-Theory; degree of approximation; integral operators; smooth kernels; eigenvalue and compactness problems of nuclear operators; operators of Hille-Tamarkin- type},

language = {eng},

number = {3},

pages = {79-118},

publisher = {Association des Annales de l'Institut Fourier},

title = {Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces},

url = {http://eudml.org/doc/74689},

volume = {35},

year = {1985},

}

TY - JOUR

AU - Carl, Bernd

TI - Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces

JO - Annales de l'institut Fourier

PY - 1985

PB - Association des Annales de l'Institut Fourier

VL - 35

IS - 3

SP - 79

EP - 118

AB - 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.

LA - eng

KW - covering problems; degree of compactness of operators; relationships between entropy moduli and Kolmogorov (resp. Gelfand and approximation) numbers; Bernstein-Jackson inequalities; Riesz-Schauder-Theory; degree of approximation; integral operators; smooth kernels; eigenvalue and compactness problems of nuclear operators; operators of Hille-Tamarkin- type

UR - http://eudml.org/doc/74689

ER -

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