MathsClub Problems, proofs & good company

The Problems

Not schoolwork — the questions that resisted Erdős, Hilbert, and everyone since. The club keeps three shelves: what is still open, what AI recently settled, and what took humanity centuries.

Tagged operator-theory — 1 entry. Clear

Does every bounded linear operator on a Hilbert space send some non-trivial closed subspace to itself? Fifty years of counterexamples on wilder spaces, two unrefereed claims on Hilbert space itself — and still no verdict.

Posed by roots in von Neumann; modern form due to Paul Halmos · 1949 · functional analysis / operator theory · difficulty 5/5

operator-theory