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

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.

Keywords

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