Arithmetic and Geometric Structures in Physics Seminar
A functional calculus allows one to apply functions to operators on Hilbert space. For instance, a classical result of Sz.-Nagy and Foias shows that every contraction $T$ on a Hilbert space without unitary summand admits an $H^\infty$-functional calculus, that is, one can make sense of $f(T)$ for every bounded analytic function $f$ in the unit disc. I will talk about a generalization of this result, which applies to tuples of commuting operators and multipliers of a large class of Hilbert function spaces on the unit ball. This is joint work with Kelly Bickel and John McCarthy.