Characterization of Fr\'{e}chet Spaces and Application to Hausdorff MNC
Functional Analysis
2020-05-06 v1
Abstract
In this short note, we give a characterization of Fr\'{e}chet spaces via properties of their metric. This allows us to prove that the Hausdorff measure of noncompactness (MNC), defined over Fr\'{e}chet spaces, is indeed an MNC. As first applications, we lift well-known fixed-point theorems for contractive and condensing operators to the setting of Fr\'{e}chet spaces.
Keywords
Cite
@article{arxiv.2005.01832,
title = {Characterization of Fr\'{e}chet Spaces and Application to Hausdorff MNC},
author = {Henning Wunderlich},
journal= {arXiv preprint arXiv:2005.01832},
year = {2020}
}