Let X be an infinite-dimensional complex normed space, and let B and S be its closed unit ball and unit sphere, respectively. We prove that the identity map on B can be expressed as an average of three uniformly retractions of B onto S. Moreover, for every 0≤ r < 1, the three retractions are Lipschitz on rB. We also show that a stronger version where the retractions are required to be Lipschitz does not hold.
@article{bwmeta1.element.bwnjournal-article-smv135i1p75bwm,
author = {A. Jim\'enez-Vargas and J. Mena-Jurado and R. Nahum and J. Navarro-Pascual},
title = {Averages of uniformly continuous retractions},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {75-81},
zbl = {0960.46012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv135i1p75bwm}
}
Jiménez-Vargas, A.; Mena-Jurado, J.; Nahum, R.; Navarro-Pascual, J. Averages of uniformly continuous retractions. Studia Mathematica, Tome 133 (1999) pp. 75-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv135i1p75bwm/
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