Leírás
Given a closed linear relation T between two Hilbert spaces H and K, the corresponding first and second coordinate projections P and Q are both linear contractions from T to H, and to K, respectively. In this talk we investigate the features of these graph contractions. We show among other things that PP*=(I+T*T)^{-1}, and that QQ*=I-(I+TT*)^{-1}. The ranges ran P* and ran Q* are proved to be closely related to the so called `regular part' of T. The connection of the graph projections to Stone's decomposition of a closed linear relation is also discussed.