Operator algebra
In functional analysis, an operator algebra is an algebra of bounded operators which is often closed in some topology. The most well-known examples include C-star algebras and von Neumann algebras; the Gelfand-Naimark theorem implies that, up to *-isomorphism, these are always operator algebras. They are also both self-adjoint: the involution operation leaves them invariant.
Examples of operator algebras which are not self-adjoint include:
- nest algebras and commutative subspace lattice algebras
- limit algebras
