Edelstein's Astonishing Affine Isometry

TL;DR

This paper revisits Edelstein's 1964 affine isometry, extending its construction and connecting it to modern optimization and monotone operator theory, highlighting its unique properties of suborbit convergence and divergence.

Contribution

It extends Edelstein's original affine isometry construction and links it to contemporary optimization and monotone operator frameworks.

Findings

Constructed an extended affine isometry with unique suborbit behavior.

Established connections to modern optimization and monotone operator theory.

Highlighted the operator's properties of suborbit convergence and divergence.

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.