Representing Diagrams and M-Ideals in L₁-Predual Spaces

We continue the study of diagrammatic representations of separable $L_1$-predual spaces and show that given an M-ideal M in a C(K)-space, there exists a diagram of C(K) such that M is given by a directed sub-diagram. Similar results are true also for the spaces $C_0(T)$, $\mathbf{c}$ and $\mathbf{c}_0$. This allows one to find a representing matrix of an M-ideal in these spaces. We also obtain some partial results for hyperplanes that are M-ideals in separable $L_1$-predual spaces.