Non-commutative holomorphic functions on Operator domains
Jim Agler, John E. McCarthy
TL;DR
This paper characterizes certain operator-valued functions that can be uniformly approximated by free polynomials on specific balanced open sets, advancing the understanding of non-commutative holomorphic functions.
Contribution
It provides a characterization of non-commutative holomorphic functions on operator domains that are approximable by free polynomials.
Findings
Functions of operator tuples approximable by free polynomials are characterized.
The work advances the theory of non-commutative holomorphic functions.
Provides tools for analyzing operator functions on balanced open sets.
Abstract
We characterize functions of -tuples of bounded operators on a Hilbert space that are uniformly approximable by free polynomials on balanced open sets.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Advanced Banach Space Theory