Abstract. In this paper we consider the problem of the existence of an interwining lifting or extension for ($*$-)regular isometric (unitary) dilations of two bicontractions. It is known that in such a generality, the commutant lifting theorem fails (see [10]). We show that such a lifting exists if the intertwining operator doubly intertwines one of the components.

AMS Subject Classification (1991): 47A20, 47A13

Keyword(s): Bicontractions, distinguished dilations, *, (-)regular dilations, intertwining operators, extensions

Received June 30, 1998, and in revised form September 9, 1999. (Registered under 2736/2009.)