The average distance property of the spaces $ \ell _\infty ^n ({\Bbb C}) $ and $ \ell _1^n ({\Bbb C}) $
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- 作者：Juan C. García-Vázquez and Rafael Villa
- 刊名：Archiv der Mathematik
- 出版年：2001
- 出版时间：March 2001
- 年：2001
- 卷：76
- 期：3
- 页码：222-230
- 全文大小：97 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Birkh盲user Basel
- ISSN：1420-8938
文摘
In this note we calculate the exact values of the rendezvous numbers of the Banach spaces l￥ n(\Bbb C) \ell _\infty ^n({\Bbb C}) and (1/3+[(2?3)/(p)]) \left({1\over 3}+{{2\sqrt 3}\over{\pi }}\right) , and l1n(\Bbb C) \ell _1^n({\Bbb C}) (given in terms of the complete elliptic integral function). This answer some questions appeared in [5]. We also consider the space \scri C (K,\Bbb C) \scri C (K,{\Bbb C}) of all \Bbb C {\Bbb C} -vlued, continous functions defined on a Hausdorff compact set K. We prove that if K has no isolated point the every a ? (1/3+[(2?3)/(p)],2) \alpha \in {\left({1\over 3}+{{2\sqrt 3}\over{\pi }},2\right)} is a rendezvous number of \scr C (K,\Bbb C) \scr C (K,{\Bbb C}) , and if K has at least one isolated point then 1/3+[(2?3)/(p)] {1\over 3}+{{2\sqrt 3}\over{\pi }} is the unique rendezvous number of \scr C (K,\Bbb C) \scr C (K,{\Bbb C}) .