[Theorem 3](http://ac.els-cdn.com/0024379585901478/1-s2.0-0024379585901478-main.pdf?_tid=07987314-f1c2-11e6-ab60-00000aab0f26&acdnat=1486972813_5a0f0539799694b806fd35a9609fa04a) provides a stronger result. Take A=B=K and specialize to k=1 in the majorization.