... x y x y （四）内积 许瓦兹不等式 线性空间(Linear space)：即向量空间； 赋范线性空间(Normed linear space)：定义了范数 的线性空间； 度量空间（Metric Space): 定义了距离的空间， 赋范线性空间也是度量空间； 内积空间(Inner product ...
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本文证明了赋范线性空间中有界齐性算子与在零点连续的齐性算子等价。
In this paper, the equivalent relation of boundedness and continuity at zero for homogeneous operator in normal linear space is proved.
本文指出了赋范线性空间上的一些局部凸拓扑的完备性与它的单位球上相应的诱导拓扑的完备性之间的关系。
The relation between the completeness of several local convex topology in normed vector space and that of induction topology of its unit ball was pointed out in this paper.
本文证明了在一定条件下赋范线性空间与其共轭空间的单位球面之间的等距算子可以延拓为全空间的实线性等距算子。
In this paper, we show that the isometry between the unit spheres of certain normed space and its dual space can be extended to a real linear isometry on the whole space.
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