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NONCOMMUTATIVE CONTINUOUS FUNCTIONS

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

Abstract

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.

Keywords

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

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Cited by

  1. A projective C-algebra related to K-theory vol.254, pp.12, 2008, https://doi.org/10.1016/j.jfa.2008.03.004
  2. From Matrix to Operator Inequalities vol.55, pp.02, 2012, https://doi.org/10.4153/CMB-2011-063-8