Please use this identifier to cite or link to this item:
|Representing matrices, M-ideals and tensor products of L₁-predual spaces
|Matriz representativa;Diagrama generalizado;Subdiagrama dirigido;M-ideales;Producto tensorial;Representing matrix;Generalized diagram;Directed sub diagram;M-ideals;Tensor products
|Universidad de Extremadura
|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.
|Appears in Collections:
|Extracta Mathematicae Vol. 33, nº 1 (2018)
This item is licensed under a Creative Commons License