On the invariant subspace problem in Hilbert spaces

TL;DR

This paper proves that every bounded linear operator on a Hilbert space possesses a non-trivial closed invariant subspace, addressing a longstanding problem in functional analysis.

Contribution

It establishes the existence of invariant subspaces for all bounded operators on Hilbert spaces, solving a major open problem.

Findings

Every bounded linear operator on a Hilbert space has a non-trivial invariant subspace.

The result applies to all operators, regardless of their specific properties.

This advances the understanding of operator structure in Hilbert spaces.

Abstract

In this paper we show that every bounded linear operator T on a Hilbert space H has a closed non-trivial invariant subspace.