Representing matrices, M-ideals and tensor products of L1-predual spaces

doi:10.17398/2605-5686.33.1.33

Authors

  • S. Dutta Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, India Department of Mathematics, Indian Institute of Technology Palakkad, India
  • D. Khurana Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, India Department of Mathematics, Indian Institute of Technology Palakkad, India
  • A. Sensarma Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, India Department of Mathematics, Indian Institute of Technology Palakkad, India

Keywords:

representing matrix, generalized diagram, directed sub diagram, M -ideals, tensor products

Abstract

Motivated by Bratteli diagrams of Approximately Finite Dimensional (AF) C* - algebras, we consider diagrammatic representations of separable L1 -predual spaces and show that, in analogy to a result in AF C* -algebra theory, in such spaces, every M-ideal corresponds to directed sub diagram. This allows one, given a representing matrix of a L1-predual space, to recover a representing matrix of an M-ideal in X. We give examples where the converse is true in the sense that given an M-ideal in a L1-predual space X, there exists a diagrammatic representation of X such that the M-ideal is given by a directed sub diagram and an algorithmic way to recover a representing matrix of M-ideals in these spaces. Given representing matrices of two L1-predual spaces we construct a representing matrix of their injective tensor product.

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References

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Published

2018-06-01

Issue

Vol. 33 No. 1 (2018)

Section

Banach Spaces and Operator Theory

How to Cite

Representing matrices, M-ideals and tensor products of L1-predual spaces : doi:10.17398/2605-5686.33.1.33. (2018). Extracta Mathematicae, 33(1), 33-50. https://revista-em.unex.es/index.php/EM/article/view/2605-5686.33.1.33

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