Journal of Convex Analysis 29 (2022), No. 2, 333--344
Copyright Heldermann Verlag 2022
Representing Diagrams and M-Ideals in L1-Predual Spaces
Pradipta Bandyopadhyay
Stat-Math Division, Indian Statistical Institute, Kolkata, India
pradipta@isical.ac.in
Aryaman Sensarma
Stat-Math Division, Indian Statistical Institute, Bangalore, India
aryamansensarma@gmail.com
We continue the study of diagrammatic representations of separable L1-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 C0(T), c and c0. 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 L1-predual spaces.
Keywords: M-ideal, L1-predual space, C(K)-space, directed sub-diagram.
MSC: 46B25, 46B20.
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