We study the inheritance of some geometric properties in a class of normed subspaces of products of normed spaces. This class includes the standard p-direct sums for $1\le p\le \infty$. We obtain necessary conditions for a space of this class to be (1) n-uniformly rotund, (2) n-uniformly rotund relative to every n-dimensional subspace and (3) n-rotund for some positive integer n. In each of the three cases, we identify a subclass such that the same conditions are sufficient for a member to have the corresponding property.

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产品空间的几何

我们研究范空间积的一类范子空间中某些几何性质的继承。此类包括标准的p直接和$\mathrm{1个}\le p\le \infty$。我们获得了此类空间的必要条件，该条件是（1）n-均匀圆形，（2）相对于每个n维子空间n-均匀圆形，（3）n-圆形对于某个正整数n。在这三种情况的每一种情况下，我们都将确定一个子类，以使相同的条件足以使成员具有相应的属性。