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bilalkadri
Joined: 12 Oct 2004
Posts: 50
Helped: 1
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 17 Dec 2004 8:36 Hilbert space |
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| What is the difference between hilbert space and a pre hilbert space.What do we mean by "if the series are all convergent" then a hilbert and a pre hilbert space are same???? any clue
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the_jackal
Joined: 15 Dec 2004
Posts: 82
Helped: 3
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| 17 Dec 2004 10:06 Re: Hilbert space |
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A Hilbert Space is a complete preHilbert
space. That is, ||v||= (v, v)½ . Not hard to prove, I omit it.
Any pre-Hilbert space that is complete is called a Hilbert space H . Complete means
that for any Cauchy sequence xn that belongs to H there exists a vector x belongs H such that xn tends to x in H,
i.e.,
||x - xn|| = 0 as n tends to infinity.[/tex]
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mayyan
Joined: 18 Aug 2001
Posts: 273
Helped: 7
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| 21 Dec 2004 8:20 Re: Hilbert space |
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about the defenition of a complete space as far as i know it say that any chushy sequence in the space converge inside the space.
[ from some N and n,m>N |Xm-Xn| --> 0 ]
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dazhen
Joined: 23 Nov 2004
Posts: 60
Helped: 2
Location: In the Mountain
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| 21 Dec 2004 17:53 Re: Hilbert space |
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mayyan,
I think you're right about the definition of completeness. But what you wrote at last is just the mathematical description of convergence of Couchy sequence. The mathematical words on completeness should be,
[Any Couchy sequence Xn in space H, for some N, n>N, |Xn-X|-->0, X  H].
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a_aziz
Joined: 04 Jan 2005
Posts: 73
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| 09 Jan 2005 11:18 Hilbert space |
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hi
I don't know what is pre hilbert space.
please give me more datails about this.
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