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arXiv · 1703.09677

A multiplier algebra functional calculus

Kelly Bickel·Michael Hartz·John E. McCarthy
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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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Kelly Bickel, Michael Hartz, John E. McCarthy. 2018-06-11. A multiplier algebra functional calculus. https://doi.org/10.1090/tran%2F7381

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