Applications of fixed point theorems in the theory of invariant subspaces

TL;DR

This paper surveys how fixed point theorems are used to establish the existence of invariant subspaces in Banach space operators, highlighting their theoretical significance.

Contribution

It provides a comprehensive overview of fixed point theorem applications in invariant subspace theory, emphasizing their role in proving existence results.

Findings

Fixed point theorems can be effectively applied to identify invariant subspaces.

The survey consolidates various methods and results in the field.

Applications span multiple classes of operators on Banach spaces.

Abstract

We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator on a Banach space.