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On the range of completely bounded maps

International Journal of Mathematics and Mathematical Sciences
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  • Mathematics


It is shown that if every bounded linear map from a C*-algebra α to a von Neumann algebra β is completely bounded, then either α is finite-dimensional or β⫅𝒞⊗Mn, where 𝒞 is a commutative von Neumann algebra and Mn is the algebra of n×n complex matrices.

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