Journal article
Extensions and extremality of recursively generated weighted shifts
Proceedings of the American Mathematical Society, Vol.130(2), pp.565-576
01/01/2002
DOI: 10.1090/S0002-9939-01-06079-8
Abstract
Given an n-step extension α : xn, ⋯, x1, (α0, ⋯, αk)∧ of a recursively generated weight sequence (0 < α0 < ⋯ < αk), and if Wα denotes the associated unilateral weighted shift, we prove that Wα is subnormal ⇔ Wα is ([k+1/2] + 1)-hyponormal (n = 1), Wα is ([k+1/2] + 2)-hyponormal (n > 1). In particular, the subnormality of an extension of a recursively generated weighted shift is independent of its length if the length is bigger than 1. As a consequence we see that if α(x) is a canonical rank-one perturbation of the recursive weight sequence α, then subnormality and k-hyponormality for Wα(x) eventually coincide. We then examine a converse-an "extremality" problem: Let α(x) be a canonical rank-one perturbation of a weight sequence a and assume that (k + 1)-hyponormality and k-hyponormality for Wα(x) coincide. We show that α(x) is recursively generated, i.e., Wα(x) is recursive subnormal.
Details
- Title: Subtitle
- Extensions and extremality of recursively generated weighted shifts
- Creators
- Raúl E. Curto - University of Iowa, MathematicsIl Bong Jung - Kyungpook National UniversityWoo Young Lee - Seoul National University
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.130(2), pp.565-576
- DOI
- 10.1090/S0002-9939-01-06079-8
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Publisher
- American Mathematical Society
- Number of pages
- 12
- Language
- English
- Date published
- 01/01/2002
- Academic Unit
- Mathematics
- Record Identifier
- 9983985962102771
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