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Averages of uniformly continuous retractions. (English) Zbl 0960.46012
It is shown that for an infinite-dimensional complex normed space the identity map on its closed unit ball $$B$$ can be expressed as the average of three continuous retractions of $$B$$ onto the unit sphere. For $$0\leq r\leq 1$$, the retractions are Lipschitz on $$rB$$. However, these retractions cannot be required to be retractions onto $$B$$.

##### MSC:
 46B20 Geometry and structure of normed linear spaces
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