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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
added a bunch of textbook references:
Gerard Murphy, Section 3.4 of: $C^\ast$-algebras and Operator Theory, Academic Press 1990 (doi:10.1016/C2009-0-22289-6)
Konrad Schmüdgen, Section 8.3 of: Unbounded operator algebras and representation theory, Operator theory, advances and applications, vol. 37. Birkhäuser, Basel (1990) (doi:10.1007/978-3-0348-7469-4)
Kehe Zhu, Section 14 of: An Introduction to Operator Algebras, CRC Press 1993 (ISBN:9780849378751)
Richard V. Kadison, John R. Ringrose, Theorem 4.5.2 in: Fundamentals of the theory of operator algebras – Volume I: Elementary Theory, Graduate Studies in Mathematics 15, AMS 1997 (ISBN:978-0-8218-0819-1)
Namely you added a link to Functorial Aspects of the GNS Representation (with its own nForum thread now here).
It’s not clear to me yet that this deserves a separate entry. It looks a lot like material for a subsection.
This entry used to refer to “Ghez, Lima and Roberts” without more details. I have added pointer to:
I have expanded the proof of the standard GNS construction (here), making explicit the use(s) of the Cauchy-Schwarz inequality.
Also I added the assumption that the given state sends the star-involution to complex conjugation, which is needed to make the inner product on the resulting vector space be Hermitian.
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