Inverse and Implicit Function Theorems for Noncommutative Functions on Operator Domains
Functional Analysis
2021-08-25 v2
Abstract
We introduce a notion of a noncommutative function defined on a domain of -tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these operatorial noncommutative functions are suitably continuous in the strong operator topology, a noncommutative dilation-theoretic construction is used to show that the assumptions on their derivatives may be relaxed from boundedness below to merely injectivity.
Cite
@article{arxiv.1804.01040,
title = {Inverse and Implicit Function Theorems for Noncommutative Functions on Operator Domains},
author = {Mark E. Mancuso},
journal= {arXiv preprint arXiv:1804.01040},
year = {2021}
}
Comments
26 pages, changes to introduction and exposition, to appear in J. Operator Theory