Isometric dilations and von Neumann inequality for a class of Tuples in the polydisc
Transactions of the American Mathematical Society
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 C[z] or C[z1, z2], respectively. However, in general, neither the existence of isometric dilation nor the von Neumann inequality holds for n-tuples, n ≥ 3, of commuting contractions. The goal of this paper is to provide a taste of isometric dilations, von Neumann inequality, and a refined version of von Neumann inequality for a large class of n-tuples, n≥3, of commuting contractions.
Barik, Sibaprasad; Krishna Das, B.; Haria, Kalpesh J.; and Sarkar, Jaydeb, "Isometric dilations and von Neumann inequality for a class of Tuples in the polydisc" (2019). Journal Articles. 1036.