# Gelfand-Naimark representation theorem

Theorem 1.1

Every $C^{*}$-algebra is isometrically isomorphic to a norm closed *-subalgebra $\mathbb{B}_{nc}(\mathord{\mathcal{H}})$ of an algebra $\mathbb{B}(\mathord{\mathcal{H}})$ of bounded operators on some Hilbert space $\mathord{\mathcal{H}}$. In particular, every finite dimensional $C^{*}$-algebra is isomorphic to a direct sum of matrix algebras.

Title Gelfand-Naimark representation theorem GelfandNaimarkRepresentationTheorem 2013-03-22 12:57:58 2013-03-22 12:57:58 PrimeFan (13766) PrimeFan (13766) 12 PrimeFan (13766) Theorem msc 46L05 ProofOfGelfandNaimarkRepresentationTheorem