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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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Dual space of Bochner space: is there an easier proof to show they're isometric?

It is known that $[L^p(0,T;H)]^* = L^q(0,T;H^*)$. If $p=q=2$ and $H$ is a Hilbert space, is there an easier proof to show that the spaces are isometric? The proof that I know for the general case us …
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