Unitary colligations of operators in Krein spaces

A model for non-contractive functions is given, according to which every bounded analytic function coincides with the characteristic function of a suitable unitary colligation. In our construction, the function is expressed in terms of a fundamentally reducible unitary dilation of the basic operator of the colligation.The results in this paper first appeared as part of the author's doctoral thesis [13] at the Universidad Central de Venezuela, under the supervision of Mischa Cotlar. The work has been supported by the Consejo Nacional de Investigaciones Cientificas y Techológicas (CONICIT-Venezuela). I am grateful to Professor Aad Dijksma, who read an earlier version of this note and made several helpful criticisms. I also thank Professor Mischa Cotlar for his kind encouragement and Professor Alejandra Cabana for correcting the english text.