Journal article
Solution of the quadratically hyponormal completion problem
Proceedings of the American Mathematical Society, Vol.131(8), pp.2479-2489
2003
DOI: 10.1090/S0002-9939-03-07057-6
Abstract
For m ≥ 1, let α: α0< …< αmbe a collection of (m+ 1) positive weights. The Quadratically Hyponormal Completion Problem seeks necessary and sufficient conditions on a to guarantee the existence of a quadratically hyponormal unilateral weighted shift W with a as the initial segment of weights. We prove that a admits a quadratically hyponormal completion if and only if the self-adjoint m x m matrix formula math. is positive and invertible, where qk:= uk+ |s|2vk, rk:= s√wk, uk:= α2k-α2k-1, vk:= α2kα2k+ 1-α2k-1α2k-2, wk:= α2k(α2k+ 1-α2k-1)2, and, for notational convenience, α-2= α-1= 0. As a particular case, this result shows that a collection of four positive numbers α0< α1< α2< α3always admits a quadratically hyponormal completion. This provides a new qualitative criterion to distinguish quadratic hyponormality from 2-hyponormality.
Details
- Title: Subtitle
- Solution of the quadratically hyponormal completion problem
- Creators
- Raúl E CurtoWoo Young Lee
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.131(8), pp.2479-2489
- DOI
- 10.1090/S0002-9939-03-07057-6
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Language
- English
- Date published
- 2003
- Academic Unit
- Mathematics
- Record Identifier
- 9983985970202771
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