Work

Operator realizations about a matrix-centre

Year: 2025

Type: preprint

Abstract: We develop a general theory of operator realizations, or ``linear representations" of analytic functions in several non-commuting variables about a matrix-centre. In particular we show that a non-commutative function has a matrix-centre realization about any matrix tuple, $Y$, in its domain, if and only if it is a uniformly analytic non-commutative function defined in a uniformly open neighbourhood of $Y$. This extends the finite-dimensional realization theory of non-commutative rational functions maximally -- to all uniformly analytic non-commutative functions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2509.08921

Authors: Karoobi, Ali, Martin, Robert T. W., Tornes, Maximilian

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7081574471

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