Surjectivity in Fr\'echet spaces
Functional Analysis
2024-08-05 v5
Abstract
We prove surjectivity result in Fr\'echet spaces of Nash-Moser type. That is, with uniform estimates over all semimorms. Our method works for functions which are only continuous and G\^ateaux differentiable like in the recent result of Ekeland. We present the results in multi-valued setting exploring the relevant notions of map regularity.
Cite
@article{arxiv.1805.07055,
title = {Surjectivity in Fr\'echet spaces},
author = {Milen Ivanov and Nadia Zlateva},
journal= {arXiv preprint arXiv:1805.07055},
year = {2024}
}
Comments
The main correction in this version is clarifying that our definition of G\^ateaux differentiability is stronger than the standard one