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http://dx.doi.org/10.4134/JKMS.2003.40.5.789

NONCOMMUTATIVE CONTINUOUS FUNCTIONS  

Don, Hadwin (Department of Mathematics University of New Hampshire Durham)
Llolsten, Kaonga (Department of Mathematics University of New Hampshire Durham)
Ben, Mathes (Department of Mathematics University of New Hampshire Durham)
Publication Information
Journal of the Korean Mathematical Society / v.40, no.5, 2003 , pp. 789-830 More about this Journal
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;
Citations & Related Records

Times Cited By Web Of Science : 6  (Related Records In Web of Science)
Times Cited By SCOPUS : 4
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