ACTA issues

On the general intertwining lifting problem. I

Animikh Biswas, Ciprian Foias

Acta Sci. Math. (Szeged) 72:1-2(2006), 271-298

Abstract. We consider the general intertwining lifting problem as formulated in [F1] and which is connected to interpolation problems in reproducing kernel Hilbert spaces. We reduce this general problem to the case where the operators involved are $n \times n$ block upper-triangular. As a consequence, we show that the causal commutant lifting (see [FT]) and the general intertwining lifting (or extension) problems are equivalent. We also obtain a seemingly new commutant lifting result for the case where one of the operators involved is nilpotent and the other canonical block Jordan. Finally, as an application, we obtain a completely new proof for the Ceausescu--Carswell--Schubert result (see [Ce], [CaS]).

AMS Subject Classification (1991): 47A20, 47A57, 47A45

Keyword(s): Cummutant lifting, interpolation, intertwining lifting

Received May 10, 2005, and in revised form November 8, 2005. (Registered under 5921/2009.)