Consider the space B[X ⊗ Y] of operators on the tensor product X ⊗ Y of normed spaces X and Y equipped with a uniform crossnorm. Take the induced uniform norm on B[X ⊗ Y] and consider its restriction to the tensor product B[X] ⊗ 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] ⊗ B[Y].

The author thanks a referee for suggestions to improve the paper which were included in Remarks 4.2 and 4.3; especially for calling his attention to the inequality that opens the argument of Remark 4.3.