The Kernel Theorem of Hilbert–Schmidt operators

All Hilbert–Schmidt operators acting on L2-sections of a vector bundle with fiber a separable Hilbert space H over a compact Riemannian manifold M, are characterized. This is achieved by defining the vector bundle of Hilbert–Schmidt operators on H, and then making use of a classical result known as the Kernel Theorem of Hilbert–Schmidt operators.  2003 Elsevier Science (USA). All rights reserved.