Abstract
A bounded linear operator S on a Hilbert space K is said to be a n-quasi- (A, m)-isometric if
S*(n)(Sigma(0 <= k <= m)(-1)(m-k)(m k)S*(k) AS(k))S-n = 0,
for some positive operator A on K and for some positive integers m and n. This class of operators seems a natural generalization of n-quasi-m-isometric and (A, m)-isometric operators on a Hilbert space ([10, 12]). First, we extend some results obtained in several papers related to n-quasi-m-isometric operators on a Hilbert space. In particular, some structural properties of this class are established with the help of special kind of operator matrix representation associated with such operators. Then, we give a necessary and sufficient condition for an operator to be a n-quasi-(A, m)-isometry. Finally, we characterize the spectra of these operators.