Retracting a ball in ℓ_1 onto its simple spherical cap - Intrakul, Jumpot; Iampiboonvatana, Smith Yokpaisan (Topological Methods in Nonlinear Analysis, 2024)
In this article, a notion and classification of spherical caps in the sequence space _1 are introduced, and the least Lipschitz constant of Lipschitz retractions from the unit ball onto a spherical cap is defined. In addition, an approximation of this value for the specific spherical cap, the simple spherical cap, is calculated. This approximation reveals a rough relation between these values, denoted by κ(α), and the answer of the optimal retraction problem for the space _1, denoted by k_0(_1). To be precise, there exists -1< μ< 0 such that k_0(_1)≤κ(α)≤2+k_0(_1) whenever -1< α< μ; here α is the level of spherical cap.