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Minimal displacement and retraction problems in infinite-dimensional Hilbert spaces

Author: Krzysztof Bolibok
Journal: Proc. Amer. Math. Soc. 132 (2004), 1103-1111
MSC (2000): Primary 47H09, 47H10
Published electronically: September 18, 2003
MathSciNet review: 2045427
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Abstract: We give the first constructive example of a Lipschitz mapping with positive minimal displacement in an infinite-dimensional Hilbert space $H.$ We use this construction to obtain an evaluation from below of the minimal displacement characteristic in the space $H.$ In the second part we present a simple and constructive proof of existence of a Lipschitz retraction from a unit ball $B$ onto a unit sphere $S$ in the space $H$, and we improve an evaluation from above of a retraction constant $k_{0}\left ( H\right ) .$

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Additional Information

Krzysztof Bolibok
Affiliation: Institute of Mathematics, Maria Curie - Skłodowska University, 20-031 Lublin, Poland

Keywords: Lipschitz mappings, minimal displacement, Lipschitz retraction
Received by editor(s): November 6, 2001
Received by editor(s) in revised form: December 10, 2002
Published electronically: September 18, 2003
Additional Notes: This research was supported in part by KBN grant 2 PO3A 029 15
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2003 American Mathematical Society