On invariant subspaces of a linear operator

TL;DR

This paper explores the concept of invariant subspaces for unbounded linear operators, critiques existing definitions, and introduces a new, improved definition to address identified shortcomings.

Contribution

It proposes a novel definition of invariant subspaces for unbounded operators, improving upon previous formulations.

Findings

Identified limitations in current definitions

Proposed a new, more robust definition

Enhanced understanding of invariant subspaces

Abstract

We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.