I will continue to post errors and clarifications that I or others
find in this location, as well as the source.
The result is
more generally true as long as you use the same norm for the vectors
in the domain space of A*B and B, the same norm for vectors
in the range space of B and the domain space of A, and the same norm
for vectors in the range space of A*B and the range of A. In other
words, you can choose three different vector norms.