Results 1 to 2 of 2

Math Help - separability

  1. #1
    Senior Member Shanks's Avatar
    Joined
    Nov 2009
    From
    BeiJing
    Posts
    374

    separability

    I was wondering how to prove a given space is separable or not.
    take L^2 and L^\infty for example please !
    Any idea or help is appreciated !
    Last edited by Shanks; November 21st 2009 at 07:59 AM. Reason: add details
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    For L^2 you could use the fact that it's a Hilbert space, and that a Hilbert space is separable iff it has a countable orthonormal basis. L^{\infty } is not so easy as the continous functions are not dense!
    Last edited by Jose27; November 21st 2009 at 08:58 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Showing separability
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 17th 2012, 08:31 AM
  2. separability problem
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: January 16th 2012, 07:40 AM
  3. Question about separability
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 7th 2011, 06:14 AM
  4. Matrix separability preservation under conjugation!
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 24th 2010, 05:35 AM
  5. Question about separability
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 20th 2009, 10:27 PM

Search Tags


/mathhelpforum @mathhelpforum