What is operator norm?

$\mathcal L(E, F)$ denotes the space of bounded (= continuous, Year 2) linear maps with the operator norm $\vertiii T = \sup_{\norm x \leq 1}\norm{Tx}$; it is submultiplicative: $\vertiii{ST} \leq \vertiii S\,\vertiii T$. The dual is $E' = \mathcal L(E, K)$.