  Inspired by the work of G. Lu on pseudo symplectic capacities we obtain
several results on the Gromov width and the Hofer--Zehnder capacity of
Hermitian symmetric spaces of compact type. Our results and proofs extend those
obtained by Lu for complex Grassmannians to Hermitian symmetric spaces of
compact type. We also compute the Gromov width and the Hofer--Zehnder capacity
for Cartan domains and their products.
