Exercise 8, § 5

Let H be a $\mathscr{S}$-equihypocontinuous set of bilinear mappings from $E \times F$ into G (exerc. 7). For every subset $M \in \mathscr{S}$, show that H is equicontinuous in $M \times F$; moreover, for every bounded subset Q of F, the union of the sets $u(M \times Q)$, where $u$ runs through H, is bounded in G.