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Averages of uniformly continuous retractions

A. Jiménez-VargasJ. Mena-JuradoR. NahumJ. Navarro-Pascual — 1999

Studia Mathematica

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.

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