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ASYMPTOTIC PROPERTIES OF KOLMOGOROV WIDTHS

Part of: Normed linear spaces and Banach spaces; Banach lattices Approximations and expansions

Published online by Cambridge University Press:  25 March 2010

MIKHAIL I. OSTROVSKII
MIKHAIL I. OSTROVSKII*
Affiliation:
Department of Mathematics and Computer Science, St. John’s University, 8000 Utopia Parkway, Queens, NY 11439, USA (email: [email protected])
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Abstract

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We consider two problems concerning Kolmogorov widths of compacts in Banach spaces. The first problem is devoted to relations between the asymptotic behavior of the sequence of n-widths of a compact and of its projections onto a subspace of codimension one. The second problem is devoted to comparison of the sequence of n-widths of a compact in a Banach space 𝒴 and of the sequence of n-widths of the same compact in other Banach spaces containing 𝒴 as a subspace.

Keywords

absolute widthsBanach spaceKolmogorov widths

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 1 , August 2010 , pp. 10 - 17
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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