Let $H$ be the Hilbert space of square integrable complex functions and let $S \subseteq H$ be a finite set of linearly independent functions of $H$. Can someone provide me an example of a surjective linear transformation that maps every function of $H$ to a function of $(H - \text{span }S) \cup \{0\}$?
2026-04-28 21:48:56.1777412936
Example of a surjective transformation that maps to the complement of the span of a known set of functions
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The set $H-\operatorname{span} (S)$ is not a vector space, so it can't be the image of a linear transformation.