Quadratically hyponormal weighted shifts with recursive tail

Exner, George R.; Jung, Il Bong; Lee, Mi Ryeong; Park, Sun Hyun

doi:10.1016/j.jmaa.2013.05.058

Cited by 5 publications

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“…The weighted shift W α acting on 2 (N 0 ), with standard basis {e i } ∞ i=0 , is defined by W α (e i ) = α i e i+1 for all i ∈ N 0 , and extended by linearity. It is well known that W α is quadratically hyponormal if and only if W α + sW 2 α is hyponormal for any s ∈ C. We give here a much abbreviated discussion of certain standard notation and computational results in this context; for a fuller discussion, see [10] or [8] amongst others. Let P n be the orthogonal projection onto…”

Section: Preliminaries and Notationmentioning

confidence: 99%

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Backward 3-Step Extensions of Recursively Generated Weighted Shifts: A range of quadratic hyponormality

Exner

Jung

Lee

et al. 2013

Bull. Aust. Math. Soc.

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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].

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Section: Preliminaries and Notationmentioning

confidence: 99%

“…In particular, weak 2-hyponormality is referred to as quadratic hyponormality. Note that the structure of quadratically hyponormal weighted shifts has been studied at some length since 1990 (see [3,[6][7][8][9][10]).…”

Section: Introductionmentioning

confidence: 99%