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Different Forms of Operator Norms

  1. Sep 19, 2009 #1
    1. The problem statement, all variables and given/known data
    93292f81089b6a6e80cac5c1e83bc14a.png

    I was given the first definition but am not sure how to get the last 3

    2. Relevant equations

    N/A

    3. The attempt at a solution

    I tried taking sup (with restriction being llxll=1) on both sides of the inequation,
    llF(x)ll=<llFll llxll, but would eventually end up with sup(llF(x)ll ; llxll=1) = sup(llF(x)ll ; llxll=1).
    Is this the right way to start deriving those 3 equations or am I supposed to derive from the very first equation?

    Thanks for the help.
     
  2. jcsd
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