On Invariant Subspaces of Subdecomposable Operators

TL;DR

This paper proves a conjecture and introduces a new, simpler invariant subspace theorem for subdecomposable operators, extending known results with weaker conditions.

Contribution

It provides a new invariant subspace theorem for subdecomposable operators with significantly weaker and more natural conditions than previous results.

Findings

Proved the Mohebi-Radjabalipour Conjecture under additional conditions.

Established a new invariant subspace theorem for subdecomposable operators.

Unified and extended existing results in the field.

Abstract

In this paper, we prove the Mohebi-Radjabalipour Conjecture under a little additional condition, and obtain a new invariant subspace theorem for subdecomposable operators. Our main results contain known results in this topic as special cases. Moreover, the condition in our theorem is really much weaker, much simpler and much more nature than that in the known results.