Hilbert space and infinite norm vectors

seratend
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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.
 
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It won't be a hilbert space, by definition.
 
matt grime said:
It won't be a hilbert space, by definition.

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.
 
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:
matt grime said:
Yes, look up the extended complex plane. It is even compact. See also the Stone-Chech compactification of a Banach Space, for instance.

Thanks a lot.

Seratend.
 

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