ACTA issues

## On the structure of c.n.u. bi-isometries

Dan Popovici

Acta Sci. Math. (Szeged) 66:3-4(2000), 719-729
2763/2009

 Abstract. As shown by Berger, Coburn and Lebow [1] and recently rediscovered by Douglas and Foiaş [3] every c.n.u. bi-isometry is unitarily equivalent with a certain isometric pair on $H^2({\msbm T},{\cal E})$ ($\cal E$ is a Hilbert space) defined in terms of two operators on ${\cal E}$, $U$ unitary and $P$ orthogonal projection. It is our aim in this paper to characterize the structure of a double commuting c.n.u. bi-isometry related to the Wold-Słociński decomposition [10] in terms of a representative $\{U,P\}$ of its complete unitary invariant. Some results concerning the minimal unitary extension are also given. AMS Subject Classification (1991): 47A45 Received October 18, 1999. (Registered under 2763/2009.)