  We prove surjectivity of the comparison map from continuous bounded
cohomology to continuous cohomology for Hermitian Lie groups with finite
center. For general semisimple Lie groups with finite center, the same argument
shows that the image of the comparison map contains all the even generators.
Our proof uses a Hirzebruch type proportionality principle in combination with
Gromov's results on boundedness of primary characteristic classes and classical
results of Cartan and Borel on the cohomology of compact homogeneous spaces.
