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A C-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (a b) = b* a* and the C-identity ‖ aa ‖ = ‖ 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 and are extensively used in .

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