An operator

, is said to belong to k-quasi class

operator if

for some positive integer n and some positive integer k. First, we will see some properties of this class of operators and prove Weyl's theorem for algebraically k-quasi class

. Second, we consider the tensor product for k-quasi class

, giving a necessary and sufficient condition for

to be a k-quasi class

, when T and S are both non-zero operators. Then, the existence of a nontrivial hyperinvariant subspace of k-quasi class

operator will be shown, and it will also be shown that if X is a Hilbert-Schmidt operator, A and

are k-quasi class

operators such that AX = XB, then

. Finally, we will prove the spectrum continuity of this class of operators.