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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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