  The celebrated Sz.-Nagy and Foias and Ando theorems state that a single
contraction, or a pair of commuting contractions, acting on a Hilbert space
always possesses isometric dilation and subsequently satisfies the von Neumann
inequality for polynomials in $\mathbb{C}[z]$ or $\mathbb{C}[z_1, z_2]$,
respectively. However, in general, neither the existence of isometric dilation
nor the von Neumann inequality holds for $n$-tuples, $n \geq 3$, of commuting
contractions. The goal of this paper is to provide a taste of the isometric
dilations, the von Neumann inequality and a sharper version of von Neumann
inequality for a large class of $n$-tuples, $n \geq 3$, of commuting
contractions.
