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BACKWARD 3-STEP EXTENSIONS OF RECURSIVELY GENERATED WEIGHTED SHIFTS: A RANGE OF QUADRATIC HYPONORMALITY
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 89 / Issue 3 / June 2014
- Published online by Cambridge University Press:
- 20 November 2013, pp. 488-493
- Print publication:
- June 2014
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- Article
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Let
$\alpha : 1, 1, \sqrt{x} , \mathop{( \sqrt{u} , \sqrt{v} , \sqrt{w} )}\nolimits ^{\wedge } $ be a backward 3-step extension of a recursively generated weighted sequence of positive real numbers with 
$1\leq x\leq u\leq v\leq w$ and let 
${W}_{\alpha } $ be the associated weighted shift with weight sequence 
$\alpha $. The set of positive real numbers 
$x$ such that 
${W}_{\alpha } $ is quadratically hyponormal for some 
$u, v$ and 
$w$ is described, solving an open problem due to Curto and Jung [‘Quadratically hyponormal weighted shifts with two equal weights’, Integr. Equ. Oper. Theory 37 (2000), 208–231].
