| 商空间的k-端点和k-严格凸性 |
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| 引用本文： | 王宏志,段丽芬,崔云安.商空间的k-端点和k-严格凸性[J].河南师范大学学报(自然科学版),2008,36(4). |
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| 作者姓名： | 王宏志 段丽芬 崔云安 |
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| 作者单位： | 1. 通化师范学院,数学系,吉林,通化134002
2. 哈尔滨理工大学,应用科学学院,哈尔滨,150080 |
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| 摘 要： | 证明了商空间X/M单位球面上的点x]为闭单位球的k-端点的充分条件是x]与X的单位球面的交集中任一点均为闭单位球的k-端点,其中M是Banach空间X的可逼近子空间.进而推出了Banach空间X以它的可逼近子空间M为模的商空间X/M对X的k-严格凸性的继承性.同时,以由N-函数生成的Orlicz空间为例,说明了上述结论成立可逼近条件是必要的.
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| 关 键 词： | 商空间 k-端点 k-严格凸 可逼近 |
On the Extreme Point and Rotundity of Quotient Spaces |
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| WANG Hong-zhi,DUAN Li-fen,CUI Yun-an.On the Extreme Point and Rotundity of Quotient Spaces[J].Journal of Henan Normal University(Natural Science),2008,36(4). |
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| Authors: | WANG Hong-zhi DUAN Li-fen CUI Yun-an |
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| Abstract: | This paper presents that a point in the unit sphere of X/M is k-extreme point of closed unit ball if every point on x]∩S(X) is a k-extreme point of closed unit ball.Here M is subpace of Banach space X and it is proximal in X.And by it,k-rotundity of X may be lifted to the quotient space X/M if X is proximal in X.Moreover,taking the example of Orlicz space generalized N-function,it points out that the condition making the above conclusion tenable is essential in general. |
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| Keywords: | quotient space k-extreme point k-rotundity approximatibility |
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