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

On the range of completely bounded maps

Richard I. Loebl

Department of Mathematics, Wayne State University, Detroit 48202, Michigan, USA

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.