The average distance property of classical Banach spaces
Copyright policy )The average distance property of classical Banach spaces
A Banach space X has the average distance property (ADP) if there exists a unique real number r such that for each positive integer n and all x1,…,xn in the unit sphere of X there is some x in the unit sphere of X such that .It is known that l2 and l∞ have the ADP, whereas lp fails to have the ADP if 1 ≤ p < 2. We show that lp also fails to have the ADP for 3 ≤ p ≤ ∞. Our method seems to be able to decide also the case 2 < p < 3, but the computational difficulties increase as p comes closer to 2.
Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry), Banach space, average distance property, Isometric theory of Banach spaces, Classical Banach spaces in the general theory, rendezvous number
Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry), Banach space, average distance property, Isometric theory of Banach spaces, Classical Banach spaces in the general theory, rendezvous number
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