Analytic formulas for the hyperbolic distance between two contractions
Tom 66 / 1997
Annales Polonici Mathematici 66 (1997), 239-252
DOI: 10.4064/ap-66-1-239-252
Streszczenie
In this paper we give some analytic formulas for the hyperbolic (Harnack) distance between two contractions which permit concrete computations in several situations, including the finite-dimensional case. The main consequence of these formulas is the proof of the Schwarz-Pick Lemma. It modifies those given in [13] by the avoidance of a general Schur type formula for contractive analytic functions, more exactly by reducing the case to the more manageable situation when the function takes as values strict contractions.
