𝑚th roots of the identity operator and the geometry conjecture

Simons, Stephen

doi:10.1090/proc/15957

$m$th roots of the identity operator and the geometry conjecture
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Proc. Amer. Math. Soc. 150 (2022), 4315-4323 Request permission

Abstract:

In this paper, we give three different new proofs of the validity of the geometry conjecture about cycles of projections onto nonempty closed, convex subsets of a Hilbert space. The first uses a simple minimax theorem, which depends on the finite dimensional Hahn-Banach theorem. The second uses Fan’s inequality, which has found many applications in optimization and mathematical economics. The third uses three results on maximally monotone operators on a Hilbert space.

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