On maximal injective subalgebras of tensor products of von Neumann algebras
Abstract
Description
Let M_i be a von Neumann algebra, and B_i be a maximal injective von Neumann subalgebra of M_i, i=1,2. If M_1 has separable predual and the center of B_1 is atomic, e.g., B_1 is a factor, then B_1\tensor B_2 is a maximal injective von Neuamnn subalgebra of M_1\tensor M_2. This partly answers a question of Popa
15 pages, a simple proof of the main theorem (Theorem 4.1 in the new version) suggested by referee is included in the new version. Typos are corrected
15 pages, a simple proof of the main theorem (Theorem 4.1 in the new version) suggested by referee is included in the new version. Typos are corrected