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191问答库 > 赋范线性空间与Banach空间、度量空间、内积空间的，希尔伯特空间之间的关系？？？

赋范线性空间与Banach空间、度量空间、内积空间的，希尔伯特空间之间的关系？？？

2025-03-16 22:35:20

推荐回答（1个）

回答1：

Banach空间是完备的赋范线性空间。内积空间中的内积可以定义范数，反之，范数不一定非要内积来定义，所以说赋范线性空间是比内积空间更广泛的概念。距离可以用范数定义，反之，只有距离满足平移不变和齐次性才能定义一个范数，因此度量空间比赋范线性空间广泛。Hilbert空间是完备的内积空间。

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