ON THE GEOMETRIC STRUCTURE OF REGULAR DILATIONS

An important role in the spectacular progress made in the understanding of the spectral theory of nonselfadjoint operators is played by the results of B. Sz.-Nagy and C. Foias regarding the isometric dilation of a Hilbert space contraction, its geometric structure and the functional model with the aid of the characteristic function. Similar results in the study of n-tuples of commutative operators were in some respect more difficult to obtain. The results from the single operator case were easily extended for n-tuples consisting of doubly commuting operators (B. Sz.-Nagy, C. Foias [14], M. Slocinski [10]). An intermediate situation is that where the n-tuple of contractions has a regular (or *-regular) isometric dilation. It is our aim to obtain structure results for Hilbert space multicontractions having this property. For simplicity we shall work in the case n = 2.