# On the range of completely bounded maps

- Authors
- Publisher
- International Journal of Mathematics and Mathematical Sciences
- Publication Date
- Disciplines

## 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.

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