High Quality Content by WIKIPEDIA articles! In mathematics, more specifically in the theory of C*-algebras, a universal C*-algebra is one characterized by a universal property. A universal C*-algebra can be expressed as a presentation, in terms of generators and relations. One requires that the generators must be realizable as bounded operators on a Hilbert space, and that the relations must prescribe a uniform bound on the norm of each generator. For example, the universal C*-algebra generated by a unitary element u has presentation <u | u*u = uu* = 1>. By the functional calculus, this C*-algebra is the continuous functions on the unit circle in the complex plane. Any C*-algebra containing a unitary element is the homomorphic image of this universal C*-algebra.

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