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For questions involving the trace of a square matrix, i.e. the sum of the elements on the main diagonal.
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Necessary and sufficient conditions on kernels of trace-class operators
Question: Let $K \in L^2(R^n\times R^n)$. Are "explicit" necessary and sufficient conditions known such that $K$ is the kernel of some trace-class operator $A \in TC(L^2(R^n))$?
We know that $K$ is th …