Norms on Infinite Dimensional Space
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Keywords:
Norm, Infinite dimensional space, Equivalent normsAbstract
It is well known that on a finite dimensional linear space, any two norms are always equivalent. But, is the converse also true? That is if all norms on a linear space $X$ are equivalent, then is $X$ necessarily finite dimensional? In this article, we try to find the answer to this question.
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.