Approximation results on s-numbers of operators

Abstract

This article investigates the convergence properties of s-numbers of certain truncations of bounded linear operators between Banach spaces. We prove a generalized version of a known convergence result for the approximation numbers of truncations of operators, removing the restrictive assumption of separability from the underlying spaces. This generalization extends several existing results in the literature and establishes a close connection between two significant problems concerning approximation numbers. By exploring the relationships between approximation numbers and other prominent s-numbers, we also derive results on the convergence of s-numbers of truncations to those of the original operator, as applications of the generalized convergence result.