International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 2, Pages 209-215
doi:10.1155/S0161171278000241
Abstract
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.