No abstract

The article deals with isometric dilation and commutant lifting for a class of n-tuples (n ≥ 3) of commuting contractions. We show that operator tuples in the class dilate to tuples of commuting isometries of BCL type. As a consequence of such an explicit dilation, we show that their von Neumann inequality holds on a one dimensional variety of the closed unit polydisc. On the basis of such a dilation, we prove a commutant lifting theorem of Sarason's type by establishing that every commutant can be lifted to the dilation space in a commuting and norm preserving manner. This further leads us to find yet another class of n-tuples (n ≥ 3) of commuting contractions each of which possesses isometric dilation.

In this article, by considering T = (T 1 , . . . , T d ), an d-tuple of commuting con-2020 Mathematics Subject Classification. 47A13, 47A20, 47B35.

We revisit the study of ω-hypercontractions corresponding to a single weight sequence ω = {ω k } k≥0 introduced by Olofsson in [22] and find an analogue of Nagy-Foias characteristic function in this setting. Explicit construction of characteristic functions is obtained and it is shown to be a complete unitary invariant. By considering a multi-weight sequence W and W-hypercontractions we extend Olofsson's work [22] in the multi-variable setting. Model for W-hypercontractions is obtained by finding their dilations on certain weighted Bergman spaces over the polydisc corresponding to the multi-weight sequence W. This recovers and provides a different proof of the earlier work of Curto and Vasilescu [13,14] for γ-contractive multi-operators through a particular choice of multi-weight sequence.