Aronszajn's Criterion for Euclidean Space
نویسنده
چکیده
We give a simple proof of a characterization of euclidean space due to Aronszajn and derive a well-known characterization due to Jordan & von Neumann as a corollary. A norm || || on a vector space V is euclidean if there is an inner product 〈 , 〉 on V such that ||v|| = √ 〈v,v〉. Characterizations of euclidean normed spaces abound. Amir [1] surveys some 350 characterizations, starting with a wellknown classic of Jordan & von Neumann [3]: a norm is euclidean iff it satisfies the parallelogram identity:
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 119 شماره
صفحات -
تاریخ انتشار 2012