On the relation between linear n-widths and approximation numbers (Q913172)

Approximation theory is one of the important branches of mathematics developing fast in different directions currently. Here the author shows that for a compact absolutely convex subset of a normal space three things coincide: the linear n-width obtained by bounded linear rank n operators, that one obtained by arbitrary linear rank n operators and the corresponding approximation number of the associated embedding. A special version of the local convexity for spaces connected with embedding operators is used. Through a counterexample it is shown that the assumption of absoluteness made on compactness cannot be replaced by relative compactness.