Abstract
We introduce noncommutative JB*-algebras which generalize both B*-algebras and JB*-algebras and set up the bases for a representation theory of noncommutative JB*-algebras. To this end we define noncommutative JB*-factors and study the factor representations of a noncommutative JB*-algebra. The particular case of alternative B*-factors is discussed in detail and a Gelfand-Naimark theorem for alternative B*-algebras is given.
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Payá, R., Perez, J. & Rodríguez, A. Noncommutative Jordan C*-algebras. Manuscripta Math 37, 87–120 (1982). https://doi.org/10.1007/BF01239948
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DOI: https://doi.org/10.1007/BF01239948