Local Properties of Ternary Rings of Operators and Their Linking C *-Algebras

We show that some local properties (such as nuclearity, exactness, and local reflexivity) of ternary rings of operators (TROs) are closely related to the local properties of their linking C*-algebras. We also show some equivalent conditions for nuclear TROs, and show that Haagerupʹs decomposition property for completely bounded maps and Pisierʹs δ-norm can be naturally generalized to TROs.