# NONCOMMUTATIVE CONTINUOUS FUNCTIONS

• Llolsten, Kaonga ;
• Ben, Mathes
• Published : 2003.09.01
• 60 28

#### 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