Perturbations of von Neumann subalgebras with finite index (Q2810711)

\textit{R. V. Kadison} and \textit{D. Kastler} defined in [Am. J. Math. 94, 38--54 (1972; Zbl 0239.46070)] a metric on the collection of all subspaces of the bounded operators on a fixed Hilbert space. They showed that sufficiently close von Neumann algebras are of the same type and conjectured that suitably close \(C^*\)-algebras should be isomorphic. \textit{E. Christensen} proved the conjecture for injective von Neumann algebras in [Invent. Math. 43, 1--13 (1977; Zbl 0366.46050)] and for von Neumann subalgebras of a finite von Neumann algebra in [Indiana Univ. Math. J. 26, 891--904 (1977; Zbl 0395.46045)].NEWLINENEWLINEIn the paper under review, the author shows that, if \(M\) and \(N\) are subalgebras of a von Neumann algebra with finite probabilistic index in the sense of \textit{M. Pimsner} and \textit{S. Popa} [Ann. Sci. Éc. Norm. Supér. (4) 19, No. 1, 57--106 (1986; Zbl 0646.46057)] which are sufficiently close, then they are unitarily equivalent.