Separable injectivity andC*-tensor products

[摘要] LetAandBbeC*-algebras and letDbe aC*-subalgebra ofB. Weshow that ifDis separably injective then the triple(A,B,D)verifies the slice mapconjecture. As an application, we prove that the minimalC*-tensor productA⊗Bisseparably injective if and only if bothAandBare separably injective and eitherAorBis finite-dimensional.

[学科分类] 数学（综合）