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Hilbert space and infinite norm vectors

  1. Dec 17, 2004 #1
    Quickly can we define a hilbert space (H, <,>) where the vectors of this space have infinite norm? (i.e. the union of finite + infinite norm vectors form a complete space).
    If yes, can you give a link to a paper available on the web? If no, can you briefly describe why?

    Thanks in advance,

    Seratend.
     
  2. jcsd
  3. Dec 17, 2004 #2

    matt grime

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    It won't be a hilbert space, by definition.
     
  4. Dec 17, 2004 #3
    Thanks, for the precision.

    OK, so I try to reformulate my question,
    Just take a vector space E. Where we define the extended norm as an application between the vectors of E and |R+U{+oO} plus the usual norm properties.
    can we have the complete property (i.e. convergence of any cauchy sequence in this space) in this vector space?

    Thanks in advance
    Seratend.
     
  5. Dec 17, 2004 #4

    matt grime

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    Yes, look up the extended complex plane. It is even compact. See also the Stone-Chech compactification of a Banach Space, for instance.
     
    Last edited: Dec 17, 2004
  6. Dec 17, 2004 #5
    Thanks a lot.

    Seratend.
     
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