Operator realizations and analytic properties of noncommutative functions
Published on:
25 April 2024
Primary Category:
Functional Analysis
Paper Authors:
Méric L. Augat,
Robert T. W. Martin,
Eli Shamovich
Bullets
Key Details
An NC function is entire if and only if it has a compact, quasinilpotent realization
In one variable, analytic functions extend meromorphically if and only if they have compact realizations
Global uniformly meromorphic NC functions are defined as having compact realizations
The skew field of such functions lies properly between rational functions and local meromorphic germs
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AI generated summary
Operator realizations and analytic properties of noncommutative functions
This paper studies operator realizations of noncommutative (NC) functions, which are a generalization of power series to several noncommuting variables. It shows that an NC function is entire (defined on the whole NC universe) if and only if it has a compact and quasinilpotent realization. For one variable, this implies a function analytic near 0 extends meromorphically if and only if it has a compact realization. This motivates defining global uniformly meromorphic NC functions as those having compact realizations, forming a skew field properly between rational functions and local meromorphic germs.
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