Decompositions and asymptotic limit for bicontractions

The asymptotic limit of a bicontraction T (that is, a pair of commuting contractions) on a Hilbert space H is used to describe a Nagy–Foias–Langer type decomposition of T. This decomposition is refined in the case when the asymptotic limit of T is an orthogonal projection. The case of a bicontraction T consisting of hyponormal (even quasinormal) contractions is also considered, where we have ST∗=S2T∗.