Lomonosov's theorem cannot be extended to chains of four operators
| dc.creator | Troitsky, Vladimir G. | |
| dc.date | 1998-09-18 | |
| dc.date.accessioned | 2026-07-07T05:26:03Z | |
| dc.date.available | 2026-07-07T05:26:03Z | |
| dc.description | We show that the celebrated Lomonosov theorem cannot be improved by increasing the number of commuting operators. Specifically, we prove that if T is the operator on l_1 without a non-trivial closed invariant subspace constructed by C.J.Read, then there are three operators S_1, S_2 and K (non-multiples of the identity) such that T commutes with S_1, S_1 commutes with S_2, S_2 commutes with K, and K is compact. It is also shown that the commutant of T contains only series of T. | |
| dc.description | 5 pages, to appear in Proceedings of the AMS | |
| dc.identifier | https://arxiv.org/abs/math/9809100 | |
| dc.identifier | http://arxiv.org/abs/math/9809100 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77412 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47A15 | |
| dc.title | Lomonosov's theorem cannot be extended to chains of four operators | |
| dc.type | text |