Results 1 to 3 of 3

Math Help - Proof of Hilbert space being finite-dimensional

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    19

    Proof of Hilbert space being finite-dimensional

    The question is if the sequence (vn) n belong to the natural numbers N whose linear span is the Hilbert space H, then H is finite dimensional.


    These sorts of proofs always confuse me. Thanks for any help given
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    Quote Originally Posted by superpickleboy View Post
    The question is if the sequence (vn) n belong to the natural numbers N whose linear span is the Hilbert space H, then H is finite dimensional.


    These sorts of proofs always confuse me. Thanks for any help given
    Just use the Baire category theorem, with the sets A_k = span \{ v_1,...,v_k\}
    Last edited by Jose27; May 10th 2010 at 07:47 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    19
    Quote Originally Posted by Jose27 View Post
    Just use the Baire category theorem, with the sets A_k = span \{ v_1,...,v_k\}

    Never heard of that theorem before. Is there any other approach to it without the use of that theorem ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stochastic PDE, infinite dimensional Hilbert Space [HARD]
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: May 10th 2011, 07:54 AM
  2. Replies: 0
    Last Post: February 11th 2011, 06:06 AM
  3. Finite Dimensional Vector Space
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 10th 2010, 11:06 AM
  4. Replies: 1
    Last Post: February 25th 2010, 01:15 AM
  5. Replies: 1
    Last Post: October 15th 2008, 11:34 AM

Search Tags


/mathhelpforum @mathhelpforum