Institute of Mathematics, Maria Curie - Sklodowska University, 20-031 Lublin, Poland
Abstract:
We give the first constructive example of a Lipschitz mapping with positive minimal displacement in an infinite-dimensional Hilbert space We use this construction to obtain an evaluation from below of the minimal displacement characteristic in the space In the second part we present a simple and constructive proof of existence of a Lipschitz retraction from a unit ball onto a unit sphere in the space , and we improve an evaluation from above of a retraction constant