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Square summable sequences

  1. Dec 13, 2007 #1

    I have a question regarding the square summable sequences:
    I should find an example of a closed set from the square summable sequences and show that the closed set does not have an element with a min norm!
    The professor mentioned an example:
    (1+1/1 0 0 0.....)
    (0 1+1/2 0 0.....)
    (0...0 1+1/n 0........)

    this set does not have an element with min norm, but why is it a closed set in l2 ?!
  2. jcsd
  3. Dec 13, 2007 #2
    they are all isolated points.
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