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Isometries of symmetric operator spaces associated with AFD factors of typeII and symmetric vector-valued spaces

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Abstract

If ϕ is a surjective isometry of the separable symmetric operator spaceE(M, τ) associated with the approximately finite-dimensional semifinite factorM and if ∥·∥ E(M,τ) is not proportional to ∥·∥ L 2, then there exist a unitary operatorU∈M and a Jordan automorphismJ ofM such thatϕ(x)=UJ(x) for allx∈M∩E(M, τ). We characterize also surjective isometries of vector-valued symmetric spacesF((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 typeII and symmetric vector-valued spaces. Integr equ oper theory 26, 102–124 (1996). https://doi.org/10.1007/BF01229507

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