| Summary: | Abstract For positive integers m and n, an operator T∈B(H) $T \in B ( H )$ is said to be an n-quasi- [m,C] $[m,C]$-isometric operator if there exists some conjugation C such that T∗n(∑j=0m(−1)j(mj)CTm−jC.Tm−j)Tn=0 . In this paper, some basic structural properties of n-quasi- [m,C] $[m,C]$-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] $[m,C]$-isometric operator is again an n-quasi- [m,C] $[m,C]$-isometric operator. Moreover, we show that the class of n-quasi- [m,C] $[m,C]$-isometric operators is norm closed. Finally, we examine the stability of n-quasi- [m,C] $[m,C]$-isometric operator under perturbation by nilpotent operators commuting with T.
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