Abstract. Giving a detailed analysis of intertwining pairs, the categorical approach of unitary asymptotes of contractions is provided. The projection-functions connected with unitary asymptotes in the functional model are characterized. Finally, properties of quasianalytic $C_{10}$-contractions are examined in the cases, when the defect index $d_T$ is finite or the asymptotic spectral multiplicity function $\delta_*\le2$.

AMS Subject Classification (1991): 47A15, 47A45

Keyword(s): unitary asymptote, $C_{10}$-contraction, quasianalycity

Received December 22, 2011, and in revised form March 30, 2012. (Registered under 68/2011.)