  Multiplicativity of certain maximal p -> q norms of a tensor product of
linear maps on matrix algebras is proved in situations in which the condition
of complete positivity (CP) is either augmented by, or replaced by, the
requirement that the entries of a matrix representative of the map are
non-negative (EP). In particular, for integer t, multiplicativity holds for the
maximal 2 -> 2t norm of a product of two maps, whenever one of the pair is EP;
for the maximal 1 -> t norm for pairs of CP maps when one of them is also EP;
and for the maximal 1 -> 2t norm for the product of an EP and a 2-positive map.
Similar results are shown in the infinite-dimensional setting of convolution
operators on L^2(R), with the pointwise positivity of an integral kernel
replacing entrywise positivity of a matrix. These results apply in particular
to Gaussian bosonic channels.
