New associative and nonassociative Gelfand-Naimark theorems |
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| Authors: | Miguel Cabrera García Angel Rodríguez Palacios |
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| Institution: | (1) Departmento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain |
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| Abstract: | We prove that, ifA is a complex Banach algebra with a unit 1 and a conjugate-linear vector space involution* such that 1*=1 and‖a
*a‖=‖a*‖ ‖a‖ for alla inA, and ifdim(A)≥3, thenA is a C*-algebra. The two-dimensional case is also considered and described. |
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