  We call a bounded linear operator acting between Banach spaces weakly
compactly generated ($\mathsf{WCG}$ for short) if its range is contained in a
weakly compactly generated subspace of its codomain. This notion simultaneously
generalises being weakly compact and having separable range. In a comprehensive
study of the class of $\mathsf{WCG}$ operators, we prove that it forms a closed
surjective operator ideal and investigate its relations to other classical
operator ideals. By considering the $p$th long James space
$\mathcal{J}_p(\omega_1)$, we show how properties of the ideal of
$\mathsf{WCG}$ operators (such as being the unique maximal ideal) may be used
to derive results outside ideal theory. For instance, we identify the
$K_0$-group of $\mathscr{B}(\mathcal{J}_p(\omega_1))$ as the additive group of
integers.
