Let $H$ be a separable $\mathbb R$-Hilbert space and $f:H\to H$ be Fréchet differentiable. Are there "simple" conditions on $f$ that ensure that the Fréchet derivatives ${\rm D}f(x)\in\mathfrak L(H)$ are trace-class for all $x\in H$?
2026-03-25 05:18:51.1774415931
Are there simple conditions on a Fréchet differentiable function on a Hilbert space that ensure that the Fréchet derivatives are trace-class?
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