Analysis Seminar: Some relations between Schwarz-Pick type inequality and von Neumann's inequality

Abstract: We define a new pseudo-distance on a polynomial polyhedron and study a Schwarz-pick type inequality for the Schur-Agler class. In our operator theoretical approach, von Neumann’s inequality for a class of diagonalizable 2×2 matrices plays an important role rather than holomorphy. Therefore, we introduce a new class that contains the Schur-Agler class and prove a Schwarz-Pick type inequality. Moreover, we use our pseudo-distance to consider dilation theory for 2×2 matrices.

Host: John McCarthy