I found two definitions, the first one is from Olsen's book and the second one is from Lance's book.
I am quite confused with the definition. In the first definition, it mensions that the strict topology on $B(H)$, since $B(H)$ is unital, the strct topology concides with the norm topology, why should we define the strict topology on $B(H)$? Is there a error: replace the strict topology on $B(H)$ by the strcit topology on $M(A)$?
In the second definition, if $E=F$, then the statement"given by the seminorms $t\to \|tx\|, t\in L(E), x\in E$. I AM QUITE CONFUSED ！ According to the first definition, $x\in M(A)$, if we viewe $L(E)$ as $M(K(E))$, then x should belong to $K(E)$, why $x\in E$?
Almost, in the first definition you have to replace "strict topology on $\mathbb B( \mathcal H)$ by "strict topology on $A$".
This definition will then agree with the second one, i.e. the one by Lance actually well formulated.