International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 2, Pages 209-215
On the range of completely bounded maps
Department of Mathematics, Wayne State University, Detroit 48202, Michigan, USA
Received 28 March 1977
Copyright © 1978 Richard I. Loebl. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
It is shown that if every bounded linear map from a -algebra to a von Neumann algebra is completely bounded, then either is finite-dimensional or , where is a commutative von Neumann algebra and is the algebra of complex matrices.