Quadratically Hyponormal Recursively Generated Weighted Shifts

On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights

“…An operator T in L(H) is said to be weakly n-hyponormal if p(T) is hyponormal for any polynomial p with degree less than or equal to n. An operator T is polynomially hyponormal if p(T) is hyponormal for every polynomial p. In particular, the weak two-hyponormality (or weak three-hyponormality) is referred to as quadratical hyponormality (or cubical hyponormality, resp.) and has been considered in detail in [1][2][3][4][5][6][7][8][9].…”

Quadratically hyponormal weighted shifts with recursive tail

“…In [9,10,20], the recursively generated positively quadratically hyponormal weighted shifts with weight sequence α : √ v, √ w (see [22]). And also, in [15,21], the recursively generated positively quadratically hyponormal weighted shifts with weight sequence α : √…”