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Roots of the identity operator and proximal mappings: (Classical and phantom) cycles and gap vectors.
- Source :
-
Proceedings of the American Mathematical Society . Dec2022, Vol. 150 Issue 12, p5383-5395. 13p. - Publication Year :
- 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–Théra duality, and use it to characterize (classical and phantom) cycles and gap vectors of proximal mappings. [ABSTRACT FROM AUTHOR]
- Subjects :
- *HILBERT space
*CONVEX functions
*CONVEX sets
*VECTOR data
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 150
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 159596655
- Full Text :
- https://doi.org/10.1090/proc/16049