On Simultaneous Farthest Points in 𝐿∞(𝐼,𝑋)
| Autor: | Sh. Al-Sharif, M. Rawashdeh |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 2011 (2011) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 |
| DOI: | 10.1155/2011/890598 |
| Popis: | Let 𝑋 be a Banach space and let 𝐺 be a closed bounded subset of 𝑋. For (𝑥1,𝑥2,…,𝑥𝑚)∈𝑋𝑚, we set 𝜌(𝑥1,𝑥2,…,𝑥𝑚,𝐺)=sup{max1≤𝑖≤𝑚‖𝑥𝑖−𝑦‖∶𝑦∈𝐺}. The set 𝐺 is called simultaneously remotal if, for any (𝑥1,𝑥2,…,𝑥𝑚)∈𝑋𝑚, there exists 𝑔∈𝐺 such that 𝜌(𝑥1,𝑥2,…,𝑥𝑚,𝐺)=max1≤𝑖≤𝑚‖𝑥𝑖−𝑔‖. In this paper, we show that if 𝐺 is separable simultaneously remotal in 𝑋, then the set of ∞-Bochner integrable functions, 𝐿∞(𝐼,𝐺), is simultaneously remotal in 𝐿∞(𝐼,𝑋). Some other results are presented. |
| Databáze: | Directory of Open Access Journals |
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