C0(X)中的Chebyshev中心的存在性

设X是一Banach空间，Co(X)表示X中所有按范数拓扑收敛于零的序列构成的空间(赋上确界范数)．证明了Co(X)中的每个紧子集均有中心充要条件是X中每个紧子集均有中心，而且，若x满足条件(Q)，则Co(X)中的每个有界集有中心充要条件是X是拟一致凸的．据此构造了一Banach空间X满足：X的每个紧子集有中心、X满足条件(Q)和X不是拟一致凸的，这样Banach空间Co(X)中的每个紧子集有中心，但并不是每个有界集均有中心．

Existence of Chebyshev Centers in C0(X)

Given a Banach space X,let C 0(X) denote the space of all sequences in X that converge to 0 in the norm topology (equipped with the supremum norm).That a space C 0(X) admits centers for compact sets if X admits centers for compact sets is shown.Moreover,for the space X satisfying a condition (Q),each bounded set in C 0(X) admits a center if X is quasi-uniformly convexity.Knowing this,a Banach space X such that the compact subsets of X admit centers,X satisfies the condition (Q) and X is not quasi-uniformly convexity is constructed.It follows that there is Banach space C 0(X) in which all compact sets,but not all bounded sets,admit centers.