Remarks on retracting balls on spherical caps in \(c_{0}\), \(c\), \(l^{\infty }\) spaces

Kazimierz Goebel

Abstract


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.

Keywords


Retraction; Lipschitz constant; radial projection; truncation; spherical cap

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References


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DOI: http://dx.doi.org/10.17951/a.2020.74.1.45-55
Date of publication: 2020-10-20 20:08:04
Date of submission: 2020-10-11 14:18:58


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