## Topological Methods in Nonlinear Analysis

### Lipschitz retractions onto sphere vs spherical cup in a Hilbert space

#### Abstract

We prove that, in every infinite dimensional Hilbert space, there exists $t_0>-1$ such that the smallest Lipscthiz constant of retractions from the unit ball onto its boundary is the same as the smallest Lipschitz constant of retractions from the unit ball onto its $t$-spherical cup for all $t\in[-1,t_0]$.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 52, Number 2 (2018), 677-691.

Dates
First available in Project Euclid: 25 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1543114846

Digital Object Identifier
doi:10.12775/TMNA.2018.034

Mathematical Reviews number (MathSciNet)
MR3915657

Zentralblatt MATH identifier
07051686

#### Citation

Intrakul, Jumpot; Chaoha, Phichet; Wichiramala, Wacharin. Lipschitz retractions onto sphere vs spherical cup in a Hilbert space. Topol. Methods Nonlinear Anal. 52 (2018), no. 2, 677--691. doi:10.12775/TMNA.2018.034. https://projecteuclid.org/euclid.tmna/1543114846

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