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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeSep 15th 2021

for completeness, to go with U(ℋ), for the moment mainly in order to record references, such as:

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeSep 19th 2021
• (edited Sep 19th 2021)

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.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeSep 19th 2021
• (edited Sep 19th 2021)

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

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeOct 30th 2021

• Ellen Maycock Parker, The Brauer Group of Graded Continuous Trace $C^\ast$-Algebras, Transactions of the American Mathematical Society 308 1 (1988) (jstor:2000953)
• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeDec 13th 2021

for the graded version of $PU(\mathcal{H})$ I have added pointer also to

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeDec 13th 2021

These authors also point (in addition to the reference in #4) to

• E. Parker, Graded continuous trace $C^\ast$-algebras and duality, Operator algebras and topology (Craiova, 1989), 130–145, Pitman Res. Notes Math. Ser., 270.

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).