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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. ...

This is a variation of my previous question. Let $X\subset \mathbb{C}^n$ be a domain, and let $L:X\times X\to \mathbb{C}$ be such that $L(x,x)>0$, $L(y,x)=\overline{L(x,y)}$ and $L(\cdot,y)$ is ...