What does this notation mean (functional analysis)?

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  1. ttoby's Avatar
    • Vengeful, Imperial Overlord of The Student Room
    • Posts: 3,691
    What does this notation mean (functional analysis)?
    Does anyone know what the notation c_0 means?

    To put it in context, there's a question "Show that l_p is separable if 1\leq p<\infty and that c_0 is separable". The solution (for l_p) involves showing that the sequence of standard unit vectors (1,0,0,...), (0,1,0,...0),... are a countable sequence with dense linear span.

    Then it says "The case for c_0 is similar but a tiny bit easier". But that doesn't tell me what c_0 means!
  2. ghostwalker's Avatar
    • Outcast of Imrryr
    • Location: CA13
    Re: What does this notation mean (functional analysis)?
    (Original post by ttoby)
    Does anyone know what the notation c_0 means?
    From Functional Analysis by Pryce.

    c_0=\{\text{all sequences convergent to 0}\} as a subspace of l_\infty

    But don't ask me anything about it, as it's rather beyond me.
    Last edited by ghostwalker; 10-05-2012 at 07:27.
  3. ttoby's Avatar
    • Vengeful, Imperial Overlord of The Student Room
    • Posts: 3,691
    Re: What does this notation mean (functional analysis)?
    (Original post by ghostwalker)
    From Functional Analysis by Pryce.

    c_0=\{\text{all sequences convergent to 0}\} as a subspace of l_\infty

    But don't ask me anything about it, as it's rather beyond me.
    Thanks for the help! (it's not letting me rep you)
  4. ghostwalker's Avatar
    • Outcast of Imrryr
    • Location: CA13
    Re: What does this notation mean (functional analysis)?
    (Original post by ttoby)
    Thanks for the help!
    Glad it was useful; you help a lot of people on here, yourself.

    In case it comes up: c=\{\text{all convergent sequences}\}, again, of l_\infty

    it's not letting me rep you
    No sweat. Thanks for the thought.
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