JournalsprimsVol. 24, No. 4pp. 673–678

Minimizing Indices of Conditional Expectations onto a Subfactor

  • Fumio Hiai

    Abiko, Japan
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Abstract

For a pair of factors M_⊇_N, let ℰ (M, N) be the set of all conditional expectations from M onto N. We characterize _E_0 ∈ ℰ (M, N) whose index is the minimum of {Index E: E ∈ ℰ (M, N)}. When M_⊇_N are II1 factors, we establish the relation between Index _E_0 and [M:N].

Cite this article

Fumio Hiai, Minimizing Indices of Conditional Expectations onto a Subfactor. Publ. Res. Inst. Math. Sci. 24 (1988), no. 4, pp. 673–678

DOI 10.2977/PRIMS/1195174872