Edelstein's Astonishing Affine Isometry
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Publication:6349197
DOI10.1080/00029890.2021.1962151arXiv2009.07370MaRDI QIDQ6349197
Sylvain Gretchko, Walaa M. Moursi, Heinz Bauschke, Matthew Saurette
Publication date: 15 September 2020
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.
Convex programming (90C25) Monotone operators and generalizations (47H05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)
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