Perturbations of Von Neumann Subalgebras With Finite Index

In this paper, we study uniform perturbations of von Neumann subalgebras of a von Neumann algebra. Let M and N be von Neumann subalgebras of a von Neumann algebra with finite probabilistic index in the sense of Pimsner and Popa. If M and N are sufficiently close, then M and N are unitarily equivalent. The implementing unitary can be chosen as being close to the identity.