Let H be a Hilbert space and C ⊂ H be closed and convex. The mapping P: H → C known as the nearest point projection is nonexpansive (1-lipschitzian). We observed that, the natural question: "Are there nonexpansive projections Q: H → C other than P?" is neglected in the literature. Also, the answer is not often present in the "folklore" of the Hilbert space theory. We provide here the answer and discuss some facts connected with the subject.
@article{bwmeta1.element.doi-10_2478_v10062-009-0008-8,
author = {Kazimierz Goebel and Ewa S\k ed\l ak},
title = {Nonexpansive retractions in Hilbert spaces},
journal = {Annales UMCS, Mathematica},
volume = {63},
year = {2009},
pages = {83-90},
zbl = {1200.47073},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-009-0008-8}
}
Kazimierz Goebel; Ewa Sędłak. Nonexpansive retractions in Hilbert spaces. Annales UMCS, Mathematica, Tome 63 (2009) pp. 83-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-009-0008-8/
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