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.
Saddi et al. (Wed,) studied this question.