Hyponormality and subnormality for powers of commuting pairs of subnormal operators
| dc.creator | Curto, Raul E. | |
| dc.creator | Lee, Sang Hoon | |
| dc.creator | Yoon, Jasang | |
| dc.date | 2006-10-28 | |
| dc.date.accessioned | 2026-07-07T08:37:12Z | |
| dc.date.available | 2026-07-07T08:37:12Z | |
| dc.description | Let H_0 (resp. H_\infty denote the class of commuting pairs of subnormal operators on Hilbert space (resp. subnormal pairs), and for an integer k>=1 let H_k denote the class of k-hyponormal pairs in H_0. We study the hyponormality and subnormality of powers of pairs in H_k. We first show that if (T_1,T_2) is in H_1, then the pair (T_1^2,T_2) may fail to be in H_1. Conversely, we find a pair (T_1,T_2) in H_0 such that (T_1^2,T_2) is in H_1 but (T_1,T_2) is not. Next, we show that there exists a pair (T_1,T_2) in H_1 such that T_1^mT_2^n is subnormal (all m,n >= 1), but (T_1,T_2) is not in H_\infty; this further stretches the gap between the classes H_1 and H_\infty. Finally, we prove that there exists a large class of 2-variable weighted shifts (T_1,T_2) (namely those pairs in H_0 whose cores are of tensor form) for which the subnormality of (T_1^2,T_2) and (T_1,T_2^2) does imply the subnormality of (T_1,T_2). | |
| dc.identifier | https://arxiv.org/abs/math/0610888 | |
| dc.identifier | http://arxiv.org/abs/math/0610888 | |
| dc.identifier | J. Funct. Anal. 245(2007), 390-412. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140319 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 47B20; 47B37; 47A13; 28A50 | |
| dc.title | Hyponormality and subnormality for powers of commuting pairs of subnormal operators | |
| dc.type | text |