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for completeness, to go with U(ℋ), for the moment mainly in order to record references, such as:
added the statement that $PU(\mathcal{H})$ is well-pointed, which is made explicit on p. 23 of
but follows by a more general result due to Dardalat and Pennig.
added statement that $S^1 \to \mathrm{U}(\mathcal{H}) \to PU(\mathcal{H})$ is a fiber bundle. Am copying this statement also to U(H) and to coset space coprojection admitting local sections
added pointer to:
for the graded version of $PU(\mathcal{H})$ I have added pointer also to
These authors also point (in addition to the reference in #4) to
but I haven’t yet found any online trace of this article/book (I find the 1983 version of the series, but not the one from 1989).
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