  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.
