#### Title

Backward 3-step extensions of recursively generated weighted shifts

#### Publication Date

2014

#### Description

Let alpha: 1, 1, sqrt{x}, (sqrt{u}, sqrt{v}, sqrt{w})^ 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 be the associated weighted shift with weight sequence . 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].

#### Journal

Bulletin of the Australian Mathematical Society

#### Volume

79

#### First Page

88

#### Last Page

93

#### Department

Mathematics

#### Recommended Citation

Exner, George R. and Jung, Il Bong. "Backward 3-step extensions of recursively generated weighted shifts." *Bulletin of the Australian Mathematical Society* (2014)
: 88-93.