Averages of uniformly continuous retractions
Volume 135 / 1999
Studia Mathematica 135 (1999), 75-81
DOI: 10.4064/sm-135-1-75-81
Abstract
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.
