Characteristic functions and joint invariant subspaces
| dc.creator | Popescu, Gelu | |
| dc.date | 2005-12-23 | |
| dc.date.accessioned | 2026-07-07T06:55:44Z | |
| dc.date.available | 2026-07-07T06:55:44Z | |
| dc.description | Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that T is a completely non-coisometric row contraction. We establish the existence of a "one-to-one" correspondence between the joint invariant subspaces under T_1,..., T_n, and the regular factorizations of the characteristic function associated with T. In particular, we prove that there is a non-trivial joint invariant subspace under the operators T_1,..., T_n, if and only if there is a non-trivial regular factorization of the characteristic function. We also provide a functional model for the joint invariant subspaces in terms of the regular factorizations of the characteristic function, and prove the existence of joint invariant subspaces for certain classes of n-tuples of operators. We obtain criterions for joint similarity of n-tuples of operators to Cuntz row isometries. In particular, we prove that a completely non-coisometric row contraction T is jointly similar to a Cuntz row isometry if and only if the characteristic function of T is an invertible multi-analytic operator. | |
| dc.description | 35 pages | |
| dc.identifier | https://arxiv.org/abs/math/0512551 | |
| dc.identifier | http://arxiv.org/abs/math/0512551 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106376 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 47A20; 47A15 | |
| dc.title | Characteristic functions and joint invariant subspaces | |
| dc.type | text |