Nonlinear Approximation in some Sequence Spaces

Abstract

We show that approximation of an element in ℓ^p space by finite number of terms is arbitrary slow, but if we use `ℓ^q norm, with q > p, as a measure of the error, then the approximation is faster. Also, we use nonlinear approximation to characterize Lorentz spaces by the error of approximation of their elements.

Key words and phrases. Sequence space, Lorentz space, Error of approximation, Nonlinear approximation.

2000 Mathematics Subject Classification. Primary: 40F05, Secondary: 40J05; 46A45