Decompositions of Linear Maps Into Non-Separable <i>C</i>*-Algebras

Abstract

We study positive decompositions of bounded linear maps between C*-algebras. A characterization of commutative injective C*-algebras is given in terms of positive decompositions with certain norm condition of linear maps. We also provide under the Continuum Hypothesis a completely bounded map into the Calkin algebra which admits no positive decomposition.