DOI QR코드

DOI QR Code

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)
  • 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

References

  1. Grad. Texts in Math. no.39 An invitation to $C^{*}$-algebras W.Arveson
  2. Proc. Amer. math. Soc. v.4 On a class of operators A.Brown https://doi.org/10.2307/2032403
  3. Illinois J. Math. v.22 Parts of operators on Hilbert space A.Brown; C.K.Fong;D.W.Hadwin
  4. Linear spans of unitary and similarity orbits of a Hilbert space operator K.A.Davidson;L.W.Marcoux
  5. Mem. Amer. Math. Soc. v.6 no.171 Charting the operator terrain J.Ernest
  6. Indiana Univ. Math. J. v.27 Continuous functions of operators: a functional calculus D.W.Hadwin https://doi.org/10.1512/iumj.1978.27.27010
  7. Trans. Amer. Math. Soc. v.244 An asymptoic double commutant theorem for $C^{*}$-algebras D.W.Hadwin https://doi.org/10.2307/1997899
  8. Trans. Amer. Math. Soc. v.266 Non-separable approximate equivalence D.W.Hadwin https://doi.org/10.2307/1998394
  9. J. Funct. Anal. v.127 Lifting algebraic elements in $C^{*}$-algebras D.W.Hadwin https://doi.org/10.1006/jfan.1995.1018
  10. Trans. Amer. Math. Soc. v.244 Closures of direct sums of classes of operators D.W.Hadwin https://doi.org/10.2307/1997899
  11. Subnormal operators and the kaplansky density theorem D.W.Hadwin
  12. Summa Brasil. Math. v.2 Normal dilations and extensions of operators P.R.Halmos
  13. Acta. Sci. Math.(Szeged) v.25 Numerical ranges and normal dilations P.R.Halmos
  14. Indiana Univ. Math. J. v.23 Normal limits of nilpotent operators D.Herrero https://doi.org/10.1512/iumj.1974.23.23089
  15. J. Funct. Anal. v.112 $C^{*}$-algebras generated by stable relations T.A.Loring https://doi.org/10.1006/jfan.1993.1029
  16. Math. Scand. v.73 Projective $C^{*}$-algebras T.A.Loring https://doi.org/10.7146/math.scand.a-12471
  17. Pacific J. Math. v.172 Stable relations Ⅱ. Corona semiprojectivity and dimension-drop $C^{*}$-algebras T.A.Loring https://doi.org/10.2140/pjm.1996.172.461
  18. Amer. Math. Soc. Providence. v.8 Lifting solutions to perturbing problems in $C^{*}$-algebras. Fields Institude Monographs T.A.Loring
  19. Proc. Amer. Math. Soc. $C^{*}$-algebras that are only weakly semiprojective T.A.Loring
  20. Rev. Roumaine Math. Pures Appl. v.21 A non-commulative Weyl-von Neumann theorem D.Voiculescu

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