k-hyponormality of finite rank perturbations of unilateral weighted shifts
| dc.creator | Curto, Raul E. | |
| dc.creator | Lee, Woo Young | |
| dc.date | 2005-07-04 | |
| dc.date.accessioned | 2026-07-07T06:33:40Z | |
| dc.date.available | 2026-07-07T06:33:40Z | |
| dc.description | In this paper we explore finite rank perturbations of unilateral weighted shifts $W_α$. First, we prove that the subnormality of $W_α$ is never stable under nonzero finite rank pertrubations unless the perturbation occurs at the zeroth weight. Second, we establish that 2-hyponormality implies positive quadratic hyponormality, in the sense that the Maclaurin coefficients of $D_n(s):=\text{det} P_n [(W_α+sW_α^2)^*, W_α+s W_α^2] P_n$ are nonnegative, for every $n\ge 0$, where $P_n$ denotes the orthogonal projection onto the basis vectors $\{e_0,...,e_n\}$. Finally, for $α$ strictly increasing and $W_α$ 2-hyponormal, we show that for a small finite-rank perturbation $α^\prime$ of $α$, the shift $W_{α^\prime}$ remains quadratically hyponormal. | |
| dc.description | 19 pages; to appear in Trans. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0507065 | |
| dc.identifier | http://arxiv.org/abs/math/0507065 | |
| dc.identifier | Trans. Amer. Math. Soc. 357(2005), 4719-4737 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99271 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47B20, 47B35, 47B37 | |
| dc.title | k-hyponormality of finite rank perturbations of unilateral weighted shifts | |
| dc.type | text |