A multiplier algebra functional calculus

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 ${\mathbb{C}}^d$.

17 pages; minor changes

Cited by in corpus (1)

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