Approximative properties of diagonal operators in Orlicz spaces

TL;DR

This paper determines exact approximation measures like best approximation and widths for diagonal operators in Orlicz sequence spaces, enhancing understanding of their approximation properties.

Contribution

It provides the exact values of key approximation quantities for diagonal operators in Orlicz spaces, a novel contribution to functional analysis.

Findings

Exact values of best approximation, basis width, Kolmogorov's width, and n-term approximation.

Improved understanding of approximation properties in Orlicz spaces.

Results applicable to analysis of diagonal operators in functional spaces.

Abstract

We obtain the exact values of some important approximative quantities (such as, the best approximation, the basis width, Kolmogorov's width and the best $n$-term approximation) of certain sets of images of the diagonal operators in the Orlicz sequence spaces $l_M$.