On the product projection of norm one in the direct product of operator algebras
Jun Tomiyama · Tohoku Mathematical Journal · 1959
In the theory of operator algebras, the following result is known (cf.[2], [4], [9], [14]): If θι and θ 2 are normal *-homomorphisms from W*-algebras Mj and M 2 onto the other ΐ^*-algebras N x and N 2 , then there exists the unique normal *-homomorphism θ from the T^*-direct product of M 2 and M 2 , MjφMs onto that of Nj and N 2 , N^Nj such as 0θ(g) y) = θ x (x) ® Θ 2 (y).Moreover, combining this result with that of Takeda [8], it can be shown that if θι and θ 2 are *-homomorphisms from C*-algebras M x and M 2 onto the other C*-algebras Nj and N 2 there exists the unique *-homomorphism θ from the C*-direct product of M x and M 2 , Mj ® M 2 , onto that of Nj and