J. Korean Math. Soc. 2003; 40(5): 789-830
Printed September 1, 2003
Copyright © The Korean Mathematical Society.
Don Hadwin, Llolsten Kaonga, and Ben Mathes
University of New Hampshire
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
MSC numbers: Primary 45A56, 45A60, 46HL89; Secondary 46H30, 46H05
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