Generalizations of Kaplansky Theorem for some (p,k)-Quasihyponormal   Operators
  In the present paper, we generalized some notions of bounded operators to un- bounded operators on Hilbert space such as k-quasihyponormal and k-paranormal unbounded operators. Furthermore, we extend the Kaplansky theorem for normal operators to some (p; k)-quasihyponormal operators. Namely the (p; k)-quasihyponormality of the product AB and BA for two operators. 
Abdelkader Benali and Ould Ahmed Mahmoud Sid Ahmed
math.FA