Abstract
We discuss some characterizations for the quadratical hyponormal unilateral weighted shiftW α with a weight sequence α, 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 α: {ie480-1} which is a back step extension of subnormal completion ofu,v, andw with0<x<-u<v<w, and prove that the recursively weighted shiftW α is quadratically hyponormal if and only if it is positively quadratically hyponormal.
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References
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Research partially supported by KOSEF 971-0102-006-2 and the Basic Science Research Institute Program, Ministry of Education, 1997, BSRI-97-1401.