Similarity and ergodic theory of positive linear maps
| dc.creator | Popescu, Gelu | |
| dc.date | 2003-10-08 | |
| dc.date.accessioned | 2026-07-07T05:01:43Z | |
| dc.date.available | 2026-07-07T05:01:43Z | |
| dc.description | In this paper we study the operator inequality ϕ(X)\leq X and the operator equation ϕ(X)= X, where ϕis a w^*-continuous positive (resp. completely positive) linear map on B(H). We show that their solutions are in one-to-one correspondence with a class of Poisson transforms on Cuntz-Toeplitz C^*-algebras, if ϕis completely positive. Canonical decompositions, ergodic type theorems, and lifting theorems are obtained and used to provide a complete description of all solutions, when ϕ(I)\leq I. We show that the above-mentioned inequality (resp. equation) and the structure of its solutions have strong implications in connection with representations of Cuntz-Toeplitz C^*-algebras, common invariant subspaces for n-tuples of operators, similarity of positive linear maps, and numerical invariants associated with Hilbert modules over \CF_n^+, the complex free semigroup algebra generated by the free semigroup on n generators. | |
| dc.description | 37 pages, Section 6 slightly improved | |
| dc.identifier | https://arxiv.org/abs/math/0310113 | |
| dc.identifier | http://arxiv.org/abs/math/0310113 | |
| dc.identifier | J.reine angew. Math. 561 (2003), 87-129 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68781 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L07,46L55 (Primary) 47A35, 47A62, 47A63 (Secondary) | |
| dc.title | Similarity and ergodic theory of positive linear maps | |
| dc.type | text |