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On the quasi-similarity of hyponormal contractions

The main purpose of this paper is to show that if T and S are hyponormal contractions with finite defect indices, then T is quasi-similar to S if and only if their unitary parts are unitarily equivalent and their completely non-unitary (c.n.u.) parts are quasi-similar. As it turns out the proof depends on hyponor-mality only through the fact that c.n.u, hyponormal contractions are of class C.o. This is where the contraction theory of Sz.-Nagy and Foia comes into play. Along the way we also obtain other results for C o contractions which are interesting on their own. The main result in this paper partially generalizes a result of Hastings [4] for the quasi-similarity of subnormal contractions. The research here is also inspired by the recent work of Conway [1].