# Gelfand-Naimark representation theorem

## Primary tabs

Keywords:
representation
Type of Math Object:
Theorem
Major Section:
Reference

## Mathematics Subject Classification

### Re: unclear

> 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.