For positive integers m and n, an operator T ∈ B(H) is said to be an n-quasi-[m, C]-isometric operator if there exists some conjugation C such thatIn this paper, some basic structural properties of n-quasi-[m, C]-isometric operators are established with the help of operator matrix representation. As an application, we obtain that a power of an n-quasi-[m, C]-isometric operator is again an n-quasi-[m, C]-isometric operator. Moreover, we show that the class of n-quasi-[m, C]-isometric operators is norm closed. Finally, we examine the stability of n-quasi-[m, C]-isometric operator under perturbation by nilpotent operators commuting with T.
MSC: 47B20; 47A05