If two norms on an infinite dimensional vector space X make the same completion(the clousure of the vector space with respect to two norms are the same ) are they equivalent norm ? If not would you give me a counter example ?
Thanks in advance
If two norms on an infinite dimentional vector space generate the same completion (generates two isomorphic banach spaces) are they equivalent?
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functional-analysis
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0What do you mean by "make the same completion"? – 2017-02-08
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0I guess he means "closure". I kind of understand that question - do you mean for every subset of your given vector space? – 2017-02-08
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0I would assume by completion he means the metric space completion. – 2017-02-08
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0@89701407 When you say the same do you mean isomorphic as vector spaces or isomorphic as banach spaces? – 2017-02-08
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0isomorphic as banach spaces – 2017-02-08