\(\mathring{B}\)-complete sets: approximative and structural properties

DOI10.1134/S0037446622030028zbMath1506.46017OpenAlexW4281716433MaRDI QIDQ2671972

I. G. Tsar'kov, Alexey R. Alimov

Publication date: 8 June 2022

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446622030028

zbMATH Keywords

Chebyshev setasymmetric Efimov-Stechkin space\(\mathring{B}\)-complete setapproximation in asymmetric spaces\( B \)-connected set

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (9)

Some classical problems of geometric approximation theory in asymmetric spaces ⋮ Solarity and proximinality in generalized rational approximation in spaces \(C(Q)\) and \(L^p\) ⋮ Reflexivity for spaces with extended norm ⋮ Density of the points of continuity of the metric function and projection in asymmetric spaces ⋮ Connectedness in asymmetric spaces ⋮ Chebyshev sets with piecewise continuous metric projection ⋮ Chebyshev unions of planes, and their approximative and geometric properties ⋮ Strict protosuns in asymmetric spaces of continuous functions ⋮ Ball-complete sets and solar properties of sets in asymmetric spaces

Cites Work

• Relations between certain classes of sets in Banach spaces
• Efimov-Stechkin spaces
• Coproximinality of linear subspaces in generalized Minkowski spaces
• Uniform convexity in nonsymmetric spaces
• Approximatively compact sets in asymmetric Efimov-Stechkin spaces and convexity of almost suns
• Compact bilinear operators on asymmetric normed spaces
• Index of symmetry and topological classification of asymmetric normed spaces
• Properties of suns in the spaces \(L^1\) and \(C(Q)\)
• A monotone path connected Chebyshev set is a sun
• Geometric properties of Banach spaces and the existence of nearest and farthest points
• Chebyshev sets and some generalizations of them
• Smoothness of subspace sections of the unit balls of \(C(Q)\) and \(L^1\)
• Connectedness and solarity in problems of best and near-best approximation
• Functional Analysis in Asymmetric Normed Spaces
• On the convexity of $ N$-Chebyshev sets
• The Banach-Mazur theorem for spaces with an asymmetric distance
• Monotone path-connectedness of Chebyshev sets in three-dimensional spaces
• Separation axioms and covering dimension of asymmetric normed spaces
• Weakly monotone sets and continuous selection in asymmetric spaces

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