## Abstract

If ϕ is a surjective isometry of the separable symmetric operator space*E(M, τ)* associated with the approximately finite-dimensional semifinite factor*M* and if ∥·∥_{
E(M,τ)
} is not proportional to ∥·∥_{
L
}
_{2}, then there exist a unitary operator*U∈M* and a Jordan automorphism*J* of*M* such that*ϕ(x)*=*UJ(x)* for all*x∈M∩E(M, τ)*. We characterize also surjective isometries of vector-valued symmetric spaces*F((0, 1), E(M, τ))*.

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Research supported by the Australian Research Council

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Sukochev, F.A. Isometries of symmetric operator spaces associated with AFD factors of type*II* and symmetric vector-valued spaces.
*Integr equ oper theory* **26**, 102–124 (1996). https://doi.org/10.1007/BF01229507

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DOI: https://doi.org/10.1007/BF01229507