A C*-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (*a b*)* = *b** *a** and the C*-identity ‖ *a** *a* ‖ = ‖ *a* ‖<sup>2</sup>.

For bounded operators on a given Hilbert space, C*-algebras characterize topologically closed subalgebras of ${\mathcal B}({\mathcal H})$ (in operator norm), also closed under taking the adjoint operator. C*-algebras are at the heart of [tag:noncommutative-geometry] and are extensively used in [tag:mathematical-physics].