Almost invariant subspaces and operators

TL;DR

This paper presents an elementary proof of an improved version of Wagner's theorem concerning almost invariant subspaces and explores implications within Galois extensions.

Contribution

It provides a simplified proof of Wagner's theorem and applies it to derive new results in Galois theory.

Findings

Elementary proof of Wagner's theorem

Enhanced understanding of almost invariant subspaces

Applications to Galois extensions

Abstract

We give an elementary proof of an efficient version of the Wagner's theorem on almost invariant subspaces and deduce some consequences in the context of Galois extensions.