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‖². Related tags: [banach-algebras], [von-neumann-algebras], [operator-algebras], [spectral-theory].
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 ‖2.
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 noncommutative-geometry and are extensively used in mathematical-physics.
Other related tags: banach-algebras, von-neumann-algebras, operator-algebras, spectral-theory.
