A multiplier algebra functional calculus

Bickel, Kelly; Hartz, Michael; McCarthy, John

doi:10.1090/tran/7381

A multiplier algebra functional calculus
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by Kelly Bickel, Michael Hartz and John E. McCarthy PDF

Trans. Amer. Math. Soc. 370 (2018), 8467-8482 Request permission

Abstract:

This paper generalizes the classical Sz.-Nagy–Foias $H^{\infty }(\mathbb {D})$ functional calculus for Hilbert space contractions. In particular, we replace the single contraction $T$ with a tuple $T=(T_1, \dots , T_d)$ of commuting bounded operators on a Hilbert space and replace $H^{\infty }(\mathbb {D})$ with a large class of multiplier algebras of Hilbert function spaces on the unit ball in $\mathbb {C}^d$.

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