Weight centralizer expectations with finite index

摘要

Let M be a von Neumann algebra, #phi# be a faithful, normal semifinite weight on M and M~#phi# its centralizer. We characterize the conditional expectations E_#phi#: M -> M~#phi# of finite index for a faithful normal strictly semifinite weight #phi# on a semifinite von Neumann algebra M with finite dimensional center. This result is used to characterize weights #phi# such that the orbit U_#phi# = {#phi# #omicron# Ad(u) : u unitary in M} can be represented as a submanifold of M_1 (=basic extension of E_#phi# : M-> M_#phi#.