Journal article
k-hyponormality of finite rank perturbations of unilateral weighted shifts
Transactions of the American Mathematical Society, Vol.357(12), pp.4719-4737
12/2005
DOI: 10.1090/S0002-9947-05-04029-8
Abstract
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 perturbations 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):= det P n [(Wα + sW α 2}*, W α + sW α 2] Pn are nonnegative, for every n ≥ 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′ of α, the shift W α′ remains quadratically hyponormal.
Details
- Title: Subtitle
- k-hyponormality of finite rank perturbations of unilateral weighted shifts
- Creators
- Raúl E. Curto - University of Iowa, MathematicsWoo Young Lee - Seoul National University
- Resource Type
- Journal article
- Publication Details
- Transactions of the American Mathematical Society, Vol.357(12), pp.4719-4737
- DOI
- 10.1090/S0002-9947-05-04029-8
- ISSN
- 0002-9947
- Number of pages
- 19
- Grant note
- 9800931 / National Science Foundation (http://data.elsevier.com/vocabulary/SciValFunders/100000001)
- Language
- English
- Date published
- 12/2005
- Academic Unit
- Mathematics
- Record Identifier
- 9983985806002771
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