Decompositions and asymptotic limit for bicontractions
Volume 105 / 2012
Annales Polonici Mathematici 105 (2012), 43-64
MSC: Primary 47A99.
DOI: 10.4064/ap105-1-5
Abstract
The asymptotic limit of a bicontraction $T$ (that is, a pair of commuting contractions) on a Hilbert space $\mathcal{H}$ is used to describe a Nagy–Foiaş–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 $S_{T^*}=S_{T^*}^2$.
