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On the range of completely bounded mapsDOI: 10.1155/s0161171278000241 Keywords: completely bounded maps , C*-algebras , von Neumann algebras , extension of maps. Abstract: It is shown that if every bounded linear map from a C*-algebra ± to a von Neumann algebra 2 is completely bounded, then either ± is finite-dimensional or 2 ￠ … ° ’ ￠ —Mn, where ° ’ is a commutative von Neumann algebra and Mn is the algebra of n —n complex matrices.
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