Geometric and probabilistic estimates for entropy and approximation numbers of operators

DOI10.1016/0021-9045(87)90100-6zbMath0647.47035OpenAlexW2074985567MaRDI QIDQ1104530

Hermann Koenig, Carsten Schuett, Yehoram Gordon

Publication date: 1987

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(87)90100-6

zbMATH Keywords

asymptotic formuladiagonal operatorsBanach space with a 1- unconditional basisprobabilistic averagingsequences of entropy and approximation numbersspace of bounded linear mappings

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46) Approximation by arbitrary linear expressions (41A45)

Related Items

Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings, Sharp asymptotics of the Kolmogorov entropy for Gaussian measures, Interpolation of approximation numbers between Hilbert spaces, An inequality between resolvents and determinants for operators in a Banach space, Entropy numbers of diagonal operators on Orlicz sequence spaces, Approximation and entropy numbers of composition operators, Entropy numbers of finite-dimensional embeddings, Estimates of covering numbers, Entropy numbers in sequence spaces with an application to weighted function spaces, Interpolation of \(s\)-numbers and entropy numbers of operators, Approximation of entropy numbers, Eigenvalues and entropy moduli of operators in interpolation spaces, Sharp asymptotics of the metric entropy for ellipsoids, Entropy numbers of embeddings of Besov spaces in generalized Lipschitz spaces, Entropy numbers of convex hulls in Banach spaces and applications, Subspaces of Small Codimension of Finite-Dimensional Banach Spaces, Some new bounds on the entropy numbers of diagonal operators, Small deviations for a family of smooth Gaussian processes, Gelfand numbers of embeddings of Schatten classes, Gaussian approximation numbers and metric entropy, On approximation numbers of composition operators, Some estimates on entropy numbers, Entropy numbers of tensor products of operators, Entropy numbers of vector-valued diagonal operators.

Cites Work

• Some inequalities for Gaussian processes and applications
• Holomorphic semi-groups and the geometry of Banach spaces
• The dimension of almost spherical sections of convex bodies
• Symmetric structures in Banach spaces
• Ellipsoids defined by Banach ideal norms
• Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
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