Contributed talk: isometric dilations, models and refined von Neumann inequality for a class of tuples in the polydisc
It is well known that for an arbitrary n-tuple (n>2) of commuting contractions, neither the existence of isometric dilation nor the celebrated von Neumann inequality holds in general. However, both of the above are true for a single contraction or a pair of commuting contractions, due to Sz.-Nagy and Foias and Ando, respectively. In this talk, we will see a large class of n-tuples of commuting contractions which possess isometric dilations and satisfy von Neumann inequality. Moreover, we get the isometric dilations explicitly on some vector-valued Hardy space over the unit polydisc, and that helps us to refine von Neumann inequality in terms of algebraic variety in the closure of the unit polydisc in the n-dimensional complex plane. (This is a joint work with B.K. Das, Kalpesh Haria and Jaydeb Sarkar.)