Gelfand-Naimark representation theorem

The Gelfand-Naimark representation theorem is as follows:

Theorem 1.1

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

Title	Gelfand-Naimark representation theorem
Canonical name	GelfandNaimarkRepresentationTheorem
Date of creation	2013-03-22 12:57:58
Last modified on	2013-03-22 12:57:58
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	12
Author	PrimeFan (13766)
Entry type	Theorem
Classification	msc 46L05
Related topic	ProofOfGelfandNaimarkRepresentationTheorem