Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
120 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

The royal road to automatic noncommutative real analyticity, monotonicity, and convexity (1907.05875v1)

Published 12 Jul 2019 in math.FA, math.CV, and math.OA

Abstract: It was shown classically that matrix monotone and matrix convex functions must be real analytic by L\"owner 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 L\"owner and Kraus theorems over operator systems as examples, including an analogue of the "butterfly realization" of Helton-McCullough-Vinnikov for general analytic functions.

Summary

We haven't generated a summary for this paper yet.