In many sources including Wikipedia, we see that there is an antilinear isomorphism between $H$ and its dual given by $\phi(y) = \langle \cdot, y \rangle$. Why not change the definition to put $y$ in the first slot instead, and thereby get a plain old linear isomorphism?
$\endgroup$ 3 Reset to defaultWhy does riesz representation for Hilbert spaces give antilinear isomorphism
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