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
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What do you mean by "make the same completion"? – gerw Feb 08 '17 at 08:06
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I guess he means "closure". I kind of understand that question - do you mean for every subset of your given vector space? – Obriareos Feb 08 '17 at 08:08
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I would assume by completion he means the metric space completion. – Leon Sot Feb 08 '17 at 08:39
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@89701407 When you say the same do you mean isomorphic as vector spaces or isomorphic as banach spaces? – Leon Sot Feb 08 '17 at 09:07
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isomorphic as banach spaces – 89701407 Feb 08 '17 at 09:09