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I have expanded the Idea section at state on a star-algebra and added a bunch of references.
The entry used to be called “state on an operator algebra”, but I renamed it (keeping the redirect) because part of the whole point of the definition is that it makes sense without necessarily having represented the “abstract” star-algebra as a C*-algebra of linear operators.
added a little bit more to state on a star-algebra, cross-linked with pure state
Started an Examples-section (here) with making explicit the two archetypical examples (classical probability measure as state on measurable functions and element on Hilbert space as state on bounded operators).
added a sentence at the very beginning, connecting back to quantum probability theory and AQFT
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