The Kernel Theorem of Hilbert-Schmidt operators |
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Institution: | Instituto de Matemáticas, Universidad Nacional Autónoma de Mexico, Ap. post. 6-60, Cuernavaca, Mor. 62131, Mexico |
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Abstract: | 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. |
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