  This paper derives an inequality relating the p-norm of a positive 2 x 2
block matrix to the p-norm of the 2 x 2 matrix obtained by replacing each block
by its p-norm. The inequality had been known for integer values of p, so the
main contribution here is the extension to all values p >= 1. In a special case
the result reproduces Hanner's inequality. As an application in quantum
information theory, the inequality is used to obtain some results concerning
maximal p-norms of product channels.
