Differential calculus for fully matricial functions I
Operator Algebras
2023-11-09 v2
Abstract
We will introduce a cyclic derivative for fully (stably) matricial functions and study its basic properties. In particular, we will show the Poincar\'{e} lemma for stably matricial functions of certain classes. We will also position Voiculescu's framework of fully matricial functions in the context of nc functions due to Kaliuzhnyi-Verbovetskyi and Vinnikov in order to clarify the relation between the present work and previous related works.
Cite
@article{arxiv.2310.09841,
title = {Differential calculus for fully matricial functions I},
author = {Hyuga Ito},
journal= {arXiv preprint arXiv:2310.09841},
year = {2023}
}
Comments
39 pages; any comments are welcome