Recent perspectives on the Invariant Subspace Problem

TL;DR

This paper reviews recent advances in the invariant subspace problem, focusing on developments over the past 15 years related to almost-invariant subspaces, universal operators, and Banach space frameworks.

Contribution

It provides a comprehensive overview of recent progress and new results in the invariant subspace problem, highlighting key areas of research and breakthroughs.

Findings

Advances in almost-invariant subspaces

Development of universal operators

New results in Banach space contexts

Abstract

We review recent work connected with the invariant subspace problem for operators, in particular new developments in the last 15 years. In particular, we include discussions of almost-invariant subspaces, universal operators, specific classes of operators and new results in the framework of Banach spaces.