商空间的k-严格凸继承性

On the Heredity of k-Rotundity of Quotient Spaces

利用Banach空间几何理论讨论了商空间对它的原空间k-严格凸继承性问题,得到了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-严格凸性具有继承性,推广了前人的结果.同时,以一般Orlicz空间为例,说明了上述结论成立和可逼近条件是必要的.

By a geometry of Banach spaces method the characterizations over a Heredity of k-rotundity problem about a quotient space to its original space is discussed.It is presented that if X is a Banach space with k-rotundity and M is proximal in X,then the quotient space X/M has also k-rotundity.Moreove,taking the example of Orlicz space generalized any Orlicz function,it points out that the condition making the above conclusion tenable is essential in general.