Matrix norm of Kronecker product Is it true that $ \| A \otimes B \| = \|A\|\|B\| $ for any matrix norm $ \|\cdot \| $? If not, does this identity hold for matrix norms induced by $ \ell_p $ vector norms? 

On page 149 exercise 6 in book: Matrix analysis for scientists and engineers, this is true for operator norm.  You can see chapter 13 of the book by the link: http://www.siam.org/books/textbooks/OT91sample.pdf
