Universal C -Algebra
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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 . By the functional calculus, this C -algebra is the…mehr

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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 . 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.