CM-ideals and L1-matricial split faces

Abstract

We discuss the order-theoretic properties of CM-ideals in matricially order smooth∞-normed spaces. We study the relation between CM-ideals and CL-summands in the matrix duality setup. We introduce the notion of L1-matricial split faces in an L1-matricially normed space and characterize CM-ideals in a matricially order smooth∞-normed space Vin terms of the L1-matricial split face of the L1-matrix convex set{Qn(V)}