Abstract

We continue the study of diagrammatic representations of separable L1L_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 C0(T)C_0(T), c\mathbf{c} and c0\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 L1L_1-predual spaces.

Author information

Contact details are reproduced from the original publication and may be historical.

Pradipta Bandyopadhyay

Stat-Math Division, Indian Statistical Institute, Kolkata, India

pradipta@isical.ac.in

Keywords

  • M-ideal
  • L1-predual space
  • C(K)-space
  • directed sub-diagram

Mathematics Subject Classification

46B25, 46B20

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Suggested citation

P. Bandyopadhyay, A. Sensarma. “Representing Diagrams and M-Ideals in L_1-Predual Spaces.” Journal of Convex Analysis 29 (2022), No. 2, 333–344. https://doi.org/10.68381/jca29020

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press LLC.