Hilbert - Schmidt operators , nuclear spaces , kernel theorem I
نویسنده
چکیده
That is, maps from A to B∗ are given by integral kernels in (A⊗B)∗. However, the validity of this adjunction depends on existence of a genuine tensor product. We recall in an appendix the demonstration that infinitedimensional Hilbert spaces do not have tensor products. Also, we must specify the topology on the duals B∗ and (A⊗B)∗. The strongest conclusion gives these the strong topology, as colimit of Hilbert-space topologies on the duals of Hilbert spaces.
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