Representing Diagrams and M-Ideals in L ₁ -Predual Spaces

We continue the study of diagrammatic representations of separable

-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) C 0 ( T )

,

\mathbf{c} c

and

\mathbf{c}_0 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 L 1

-predual spaces.