Computing the norm of an operator, references or examples

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I am struggling a lot when I try to compute the norm of an operator. I was wondering if someone here could recommend a book/chapter/online notes/ other resource that I can look into to get a better feeling of the techniques and general ideas we use to compute the norm of an operator.

I know the definition of an operator norm is $\|T\| = \sup_{\|x\| = 1}\|Tx\| = \sup_{x \neq 0} \frac{\|Tx\|}{\|x\|}$ but that doesn't really help me when I actually need to compute this kind of stuff. Thanks for any help or resources.