Limits of an approach

  • Thread starter BDV
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  • #1
BDV
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Hello,

I have seen (in H Cartan's differential calculus) a proof that if F is a Banch space, L(E,F) where E is some vector space, is also a Banach space. One of the main points of the proof is based on the behaviour of a function being "proper" (continuous) on a ball of arbitrary radius "n" and by such being able to extend the property to the entire space.

I was wondering when/how does this type of argument fail?
 

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  • #2
mathman
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Notation question. What is L(E,F)?
 
  • #3
BDV
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I apologize, it is the space of linear functions from E to F.
 
  • #4
Erland
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Mustn't E also be a normed space? How can one otherwise talk about a ball with a certain radius in E?
 
  • #5
mathwonk
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yes, but not necessarily complete.
 

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