2-Biisometric operators in Hilbert space

In this paper, we consider a generalization of biisometric Hilbert space operators. Inspired by the work [C. Kubrusly and N. Levan, Biisometric operators and biorthogonal sequences, Bull. Korean Math. Soc. 56 (2019) 585–596], we introduce the class of [Formula: see text]-biisometric operator. A pair [Formula: see text] is said to be a [Formula: see text]-biisometry if [Formula: see text] We study many algebraic and spectral properties of this class of operators. We also characterize unilateral weighted shifts which are [Formula: see text]-biisometric operators. To illustrate the work we give some examples of 2-biisometric operators and we construct biorthogonal sequences relative to which they are shift operators.