摘要:
We discuss some characterizations for the quadratical hyponormal unilateral weighted shift W alpha with a weight sequence alpha, which give a distinction example for quadratical hyponormality and positively quadratical hyponormality. In addition, we consider a recursively quadratically hyponormal weighted shift with a recursive weight alpha : root x, (root u, root v, root w)(boolean AND) which is a back step extension of subnormal completion of u, v, and w with 0 < x less than or equal to u. < v < w, and prove that the recursively weighted shift W alpha is quadratically hyponormal if and only if it is positively quadratically hyponormal.