Open AccessRemarks on retracting balls on spherical caps in \(c_{0}\), \(c\), \(l^{\infty }\) spaces
Author(s) -
Kazimierz Goebel
Publication year - 2020
Publication title -
annales universitatis mariae curie-skłodowska. sectio a, mathematica
Language(s) - English
Resource type - Journals
eISSN - 2083-7402
pISSN - 0365-1029
DOI - 10.17951/a.2020.74.1.45-55
Subject(s) - unit sphere , banach space , lipschitz continuity , sequence (biology) , mathematics , ball (mathematics) , norm (philosophy) , pure mathematics , mathematical analysis , unit (ring theory) , space (punctuation) , combinatorics , computer science , philosophy , genetics , mathematics education , biology , operating system , epistemology
For any infinite dimensional Banach space there exists a lipschitzian retraction of the closed unit ball B onto the unit sphere S. Lipschitz constants for such retractions are, in general, only roughly estimated. The paper is illustrative. It contains remarks, illustrations and estimates concerning optimal retractions onto spherical caps for sequence spaces with the uniform norm.