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This question was also formerly posted on MSE but has not received any answer or comment. Let $H$ be the infinite-dimensional seperable complex Hilbert space, and $P(H)$ denote its projectivization. ...

Let $G$ be a connected domain in $\mathbb{C}^{n}$, let $H$ be a Hilbert space and let $f,g:G\to H\backslash \{0\}$ be holomorphic (in my particular situation they are also injective, but I don't think ...