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In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties:

A is a topologically closed set in the norm topology of operators.
A is closed under the operation of taking adjoints of operators.

Another important class of non-Hilbert C*-algebras includes the algebra C_0(X) of complex-valued continuous functions on X that vanish at infinity, where X is a locally compact Hausdorff space. C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables. This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933. Subsequently, John von Neumann attempted to establish a general f

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Summary

A is a topologically closed set in the norm topology of operators.
A is closed under the operation of taking adjoints of operators.

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