On m-Biisometric operators on a Hilbert space

A pair of operators [Formula: see text] is said to be an [Formula: see text]-biisometric operator (or an [Formula: see text]-biisometry) if it satisfies the equation [Formula: see text] In this paper, we first present several properties associated with this family. Then, we prove that if [Formula: see text] is an [Formula: see text]-biisometry and [Formula: see text] are nilpotent operators with order [Formula: see text] and [Formula: see text] respectively, then [Formula: see text] is [Formula: see text]-biisometric operator where [Formula: see text]. Finally, we characterize the spectra of these operators.