On Simultaneous Farthest Points in ๐ฟโ(๐ผ,๐)
Let ๐ be a Banach space and let ๐บ be a closed bounded subset of ๐. For (๐ฅ1,๐ฅ2,โฆ,๐ฅ๐)โ๐๐, we setโโ๐(๐ฅ1,๐ฅ2,โฆ,๐ฅ๐,๐บ)=sup{max1โค๐โค๐โ๐ฅ๐โ๐ฆโโถ๐ฆโ๐บ}. The set ๐บ is called simultaneously remotal if, for any (๐ฅ1,๐ฅ2,โฆ,๐ฅ๐)โ๐๐, there exists ๐โ๐บ such thatโโ๐(๐ฅ1,๐ฅ2,โฆ,๐ฅ๐,๐บ)=max1โค๐โค๐โ๐ฅ๐โ๐โ. In this paper, we show that if...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/890598 |
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| Summary: | Let ๐ be a Banach space and let ๐บ be a closed bounded subset of ๐. For (๐ฅ1,๐ฅ2,โฆ,๐ฅ๐)โ๐๐, we setโโ๐(๐ฅ1,๐ฅ2,โฆ,๐ฅ๐,๐บ)=sup{max1โค๐โค๐โ๐ฅ๐โ๐ฆโโถ๐ฆโ๐บ}. The set ๐บ is called simultaneously remotal if, for any (๐ฅ1,๐ฅ2,โฆ,๐ฅ๐)โ๐๐, there exists ๐โ๐บ such thatโโ๐(๐ฅ1,๐ฅ2,โฆ,๐ฅ๐,๐บ)=max1โค๐โค๐โ๐ฅ๐โ๐โ. In this paper, we show that if ๐บ is separable simultaneously remotal in ๐, then the set of โ-Bochner integrable functions, ๐ฟโ(๐ผ,๐บ), is simultaneously remotal in ๐ฟโ(๐ผ,๐). Some other results are presented. |
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| ISSN: | 0161-1712 1687-0425 |