Averages of uniformly continuous retractions. (English) Zbl 0960.46012

Jiménez-Vargas, A.; Mena-Jurado, J. F.; Nahum, R.; Navarro-Pascual, J. C.

Stud. Math. 135, No. 1, 75-81 (1999).

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 \(B\).

Reviewer: J.H.M.Whitfield (Thunder Bay)

MSC:

46B20

Geometry and structure of normed linear spaces

Keywords:

uniformly continuous; averages; retractions; continuous retractions