Operational independence and tensor products of C*-algebras

Complete C*-independence of operator algebras is introduced. Equivalent characterization is given for C*-subalgebras to be completely independent in terms of maximal tensor product. Besides, the independence of Banach algebras is considered, and we showed that Hahn-Banach independence is a generalization of C*-independence and discussed Hahn-Banach independence in M-n(A), where A is a C*-algebra. Among others, we characterize independence of operator algebras by projective and injective C*-tensor product in terms of simultaneous extensions of completely positive maps. Published by AIP Publishing.