A multiplier algebra functional calculus.
This paper generalizes the classical Sz.-Nagy–Foias H∞(D) functional calculus for Hilbert space contractions. In particular, we replace the single contraction T with a tuple T = (T1,...,Td) of commuting bounded operators on a Hilbert space and replace H∞(D) with a large class of multiplier algebras of Hilbert function spaces on the unit ball in Cd.
Transactions of the American Mathematical Society
Link to OA full text
Kelly Bickel, Michael Hartz and John E. McCarthy. Trans. Amer. Math. Soc. 370 (2018), 8467-8482