• Don, Hadwin ;
  • Llolsten, Kaonga ;
  • Ben, Mathes
  • Published : 2003.09.01


By forming completions of families of noncommutative polynomials, we define a notion of noncommutative continuous function and locally bounded Borel function that give a noncommutative analogue of the functional calculus for elements of commutative $C^{*}$-algebras and von Neumann algebras. These notions give a precise meaning to $C^{*}$-algebras defined by generator and relations and we show how they relate to many parts of operator and operator algebra theory.


functional calculus;$C^{*}$-algebra;von Neumann algebra;noncommutative continuous function;stable relations;parts of operators


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