Riv.Mat.Univ.Parma (6) 2* (1999)


Up and down along rays

Pages 171-189
Received: 22 September 1999
Mathematics Subject Classification (2000): 46B99 - 46C15 - 41A44

Supported by MURST

Abstract We consider radial motions of points in real normed spaces. Radial projections, i.e. retractions of points of the space onto the unit ball, have been studied extensively: in fact, the radial projection constant is, among all parameters, one of the most studied. Recall that radial projections are seldom nonexpansive (outside the case of norms defined by inner products). We consider here also other displacements along radial directions: for example, radial projections onto the unit sphere both from inside and from outside (or sending points at the same distance from the origin). We study the best constants by which these radial movements can be controlled.

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