Analysis Seminar: "Matrix Monotonicity in the Quasi-Rational Setting"
Abstract: In this talk, we will show quasi-rational functions on the bidisk D^2 (intuitively, inner functions that are rational in one of the variables) yield functions that preserve matrix inequalities on rectangles in R^2. This result proves a special case of a 2012 conjecture posed by Agler, McCarthy, and Young about local-to-global matrix monotonicity of two-variable functions. The main tools include (1) concrete realization formulas with nice boundary behavior, (2) formulas that allow one to change realization domains without adding unnecessary singularities, and (3) recent advances in non-commutative function theory. This is joint work with J.E. Pascoe and Ryan Tully-Doyle.
Host: John McCarthy