A C*-algebra is a Banach algebra together with an isometric involution satisfying (ab)* = b*a* and the C*-identity |a*a| = |a|^2. This characterizes the closed subalgebras of the bounded operators on Hilbert space, closed under taking the adjoint operator. They are at the heart of (spectral-theory) and are extensively used in (mathematical-physics) and (non-commutative-geometry). Related tags: (banach-algebras), (von-neumann-algebras), (operator-algebras).
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