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Thread: separability

  1. November 20th 2009, 11:23 PM #1
    Shanks
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    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
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  2. November 21st 2009, 08:38 AM #2
    Jose27
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    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.
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