  We investigate quantization properties of Hermitian metrics on holomorphic
vector bundles over homogeneous compact K\"ahler manifolds. This allows us to
study operators on Hilbert function spaces using vector bundles in a new way.
We show that Yang--Mills metrics can be quantized in a strong sense and for
equivariant vector bundles we deduce a strong stability property which
supersedes Gieseker-stability. We obtain interesting examples of generalized
notions of contractive, isometric, and subnormal operator tuples which have
geometric interpretations related to holomorphic vector bundles over coadjoint
orbits.
