  Consider the space $B[X\otimes_\alpha Y]$ of operators on the tensors product
${X\otimes_\alpha Y}$ of normed spaces $X$ and $Y$ equipped with a uniform
crossnorm ${\|\cdot\|_\alpha}$$.$ Take the induced uniform norm on
$B[X\otimes_\alpha Y]$ and consider its restriction to the tensor product
${B[X]\otimes B[Y]}$ of the algebra of operators $B[X]$ and $B[Y].$ It is
proved that such a restriction is a reasonable crossnorm on ${B[X]\otimes
B[Y]}$.
