Lomonosov’s theorem cannot be extended to chains of four operators
Lomonosov’s theorem cannot be extended to chains of four operators
We show that the celebrated Lomonosov theorem cannot be improved by increasing the number of commuting operators. Specifically, we prove that if $T\colon \ell _1\to \ell _1$ is the operator without a non-trivial closed invariant subspace constructed by C. J. Read, then there are three operators $S_1$, $S_2$ and $K$ …