Geodesic
Averages of uniformly continuous retractions
Studia Mathematica, Tome 135 (1999) no. 1, pp. 75-81

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-135-1-75-81
Keywords: uniformly retraction, Lipschitz retraction, extreme point

A. Jiménez-Vargas 1 ;  1 ;  1 ;  1

1 
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A. Jiménez-Vargas;  ;  ;  . Averages of uniformly continuous retractions. Studia Mathematica, Tome 135 (1999) no. 1, pp. 75-81. doi: 10.4064/sm-135-1-75-81

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