Matrix algebras with multiplicative decomposition property (Q624350)

The authors consider the multiplicative decomposition property (the multiplicative analogue of the Riesz decomposition property) for entry-wise ordered matrix algebras over the reals. They characterize for which matrix pairs such a decomposition exists and use this result to present necessary and sufficient conditions for a matrix algebra to enjoy the decomposition property by all its positive matrix pairs. Thus they describe all matrix algebras with the decomposition property.