Abstract: 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 multiplier algebras of a large class of Hilbert function spaces on the unit ball. In particular, this extends a recent theorem of Clou^atre and Davidson for commuting row contractions. This is joint work with Kelly Bickel and John McCarthy.
Host: John McCarthy