Lomonosov’s Theorem Cannot Be Extended to Chains of Four Operators

@inproceedings{TROITSKY1998LomonosovsTC,
  title={Lomonosov’s Theorem Cannot Be Extended to Chains of Four Operators},
  author={VLADIMIR G. TROITSKY and V. G. TROITSKY},
  year={1998}
}
  • VLADIMIR G. TROITSKY, V. G. TROITSKY
  • Published 1998
We show that the celebrated Lomonosov theorem cannot be improved by increasing the number of commuting operators. Specifically, we prove that if T : `1 → `1 is the operator without a non-trivial closed invariant subspace constructed by C. J. Read, then there are three operators S1, S2 and K (non-multiples of the identity) such that T commutes with S1, S1… CONTINUE READING