Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Reference14 articles.
1. Diameters of sets in functional spaces and the theory of best approximations;Tikhomirov;Uspekhi Mat. Nauk,1960
2. Absolute Widths of Some Embeddings
3. The widths of certain finite-dimensional sets and classes of smooth functions;Kashin;Izv. Akad. Nauk SSSR Ser. Mat.,1977
4. n-Widths in Approximation Theory
5. On the approximation numbers of an operator and its adjoint