Roots of the identity operator and proximal mappings: (classical and phantom) cycles and gap vectors

DOI10.1090/PROC/16049arXiv2201.05189WikidataQ114094163 ScholiaQ114094163MaRDI QIDQ6388215

Publication date: 13 January 2022

Abstract: Recently, Simons provided a lemma for a support function of a closed convex set in a general Hilbert space and used it to prove the geometry conjecture on cycles of projections. In this paper, we extend Simons's lemma to closed convex functions, show its connections to Attouch-Thera duality, and use it to characterize (classical and phantom) cycles and gap vectors of proximal mappings.

Mathematics Subject Classification ID

Convex programming (90C25) Monotone operators and generalizations (47H05) Set-valued and variational analysis (49J53) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Fixed-point theorems (47H10) Convex functions and convex programs in convex geometry (52A41)

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