On the Problem of Retracting Balls onto Their Boundary
نویسنده
چکیده
Let (X,‖ · ‖) be an infinite-dimensional Banach space with the unit ball B and the unit sphere S. Since the works of Nowak [11], Benyamini and Sternfeld [1], and Lin and Sternfeld [10], it is known that S is a Lipschitzian retract of B. It means that there exists a mapping (retraction) R : B → S satisfying Rx = x for all x ∈ S and also being Lipschitzian. If R satisfies the Lipschitz condition with constant k (R∈ (k)),
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