Schauder's Theorem and s-Numbers

TL;DR

This paper explores the relationship between s-numbers of an operator and its adjoint in Banach spaces, extending Schauder's classical theorem to a broader context.

Contribution

It provides new insights into how s-numbers of an operator relate to those of its adjoint, generalizing Schauder's theorem in Banach space theory.

Findings

Established connections between s-numbers of T and T*

Extended Schauder's theorem to s-number context

Provided new bounds and inequalities for s-numbers

Abstract

Motivated by the well known theorem of Schauder, we study the relationship between various s-numbers of an operator T and its adjoint T* between Banach spaces.