Edelstein's Astonishing Affine Isometry
Functional Analysis
2020-09-17 v1 Optimization and Control
Abstract
In 1964, Michael Edelstein presented an amazing affine isometry acting on the space of square-summable sequences. This operator has no fixed points, but a suborbit that converges to 0 while another escapes in norm to infinity! We revisit, extend and sharpen his construction. Moreover, we sketch a connection to modern optimization and monotone operator theory.
Cite
@article{arxiv.2009.07370,
title = {Edelstein's Astonishing Affine Isometry},
author = {Heinz H. Bauschke and Sylvain Gretchko and Walaa M. Moursi and Matthew Saurette},
journal= {arXiv preprint arXiv:2009.07370},
year = {2020}
}