Slant Toeplitz operators on the Lebesgue space of $n$-dimensional torus

Abstract

In this paper, we introduce the $k$-th order slant Toeplitz operator on the Lebesgue space $L^2(\mathbb{T}^n)$ for a fixed integer $k\ge2$ and also investigate certain algebraic properties of the $k$-th order slant Toeplitz operator on the Lebesgue space $L^2(\mathbb{T}^n)$. The complete characterization of the $k$-th order slant Toeplitz operator is also given. Finally, norms and the spectral radius of the introduced operator are discussed.