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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Minimal displacement and retraction problems in infinite-dimensional Hilbert spaces
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by Krzysztof Bolibok PDF
Proc. Amer. Math. Soc. 132 (2004), 1103-1111 Request permission

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
  • Email: bolibok@golem.umcs.lublin.pl
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1103-1111
  • MSC (2000): Primary 47H09, 47H10
  • DOI: https://doi.org/10.1090/S0002-9939-03-07150-8
  • MathSciNet review: 2045427