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Compact Operators on a Hilbert Space

  1. Jul 12, 2010 #1
    Hello, I hope I am asking this in the right area of the forums. I wanted to ask if the following formula is true (assuming H is infinite dimensional and separable):

    [tex] \mathcal{K} (\mathcal{H}) \approx \mathcal{K} (\mathcal{H} \oplus \mathcal{H} \oplus \mathcal{H} \oplus \mathcal{H})\approx M_{4} (\mathcal{K} (\mathcal{H})) [/tex]

    I'm pretty sure this is true, but I am worried I am crazy, because I don't understand how every compact operator could secretly be 16 compact operators
     
    Last edited: Jul 12, 2010
  2. jcsd
  3. Jul 12, 2010 #2

    Hurkyl

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    Please only post a question once.
     
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