# Different Forms of Operator Norms

1. Sep 19, 2009

### maritimer

1. The problem statement, all variables and given/known data

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.