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Gelfand-Naimark representation theorem

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Mathematics Subject Classification

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> First, what do you mean by "closed *-subalgebra"?
> Specifically, does "closed" refer to some topology
> imposed on the algebra?

Yes, C*-algebras are topological algebras, so norm closed.

> Also, you use notation without explaining what it means.
> For examle, what is B(H)? My best guess is that it is
> algebra of bounded operators on a Hilbert space. Whatever
> it represents, it should be explained.

You're right, this is standard notation. I wasn't sure of the best way to deal with this. I was thinking along the lines of having an entry on bounded operators, and then linking to that. But, it won't hurt to be explicit here.

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