Abstract:

It is well known that for an arbitrary

*n*-tuple (*n*> 2) of commuting contractions, neither isometric dilation exists nor the celebrated von Neumann inequality holds in general. However, both of the above are true for a single contraction or for a pair of commuting contractions, due to Sz.-Nagy and Ando, respectively. In this talk, we will discuss a class of*n*-tuples of commuting contractions which possess isometric dilations and satisfy von Neumann inequality. We will see that the dilations are explicit on some vector-valued Hardy space over the unit polydisc, and for some particular tuples in this class, the explicitness helps us to refine von Neumann inequality in terms of an algebraic variety in the closure of the unit polydisc in the*n*-dimensional complex plane.(This is a joint work with Bata Krishna Das, Kalpesh Haria and Jaydeb Sarkar)