Journal article
The royal road to automatic noncommutative real analyticity, monotonicity, and convexity
Advances in mathematics (New York. 1965), v 407, 108548
08 Oct 2022
Abstract
It was shown classically that matrix monotone and matrix convex functions must be real analytic by Löwner and Kraus respectively. Recently, various analogues have been found in several noncommuting variables. We develop a general framework for lifting automatic analyticity theorems in matrix analysis from one variable to several variables, the so-called “royal road theorem.” That is, we establish the principle that the hard part of proving any automatic analyticity theorem lies in proving the one variable theorem. We use our main result to prove the noncommutative Löwner and Kraus theorems over operator systems as examples, including an analogue of the rational “butterfly realization” of Helton-McCullough-Vinnikov for general analytic functions.
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Details
- Title
- The royal road to automatic noncommutative real analyticity, monotonicity, and convexity
- Creators
- J.E. Pascoe - University of FloridaRyan Tully-Doyle - California State Polytechnic University
- Publication Details
- Advances in mathematics (New York. 1965), v 407, 108548
- Publisher
- Elsevier
- Grant note
- Fields Institute
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000835724300019
- Scopus ID
- 2-s2.0-85134583570
- Other Identifier
- 991021879785104721
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Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics