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Approximation of normal elements in the multiplier algebra of an AF $ C\sp *$-algebra

Authors: Terry A. Loring and Jack Spielberg
Journal: Proc. Amer. Math. Soc. 121 (1994), 1173-1175
MSC: Primary 46L05
MathSciNet review: 1211584
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Abstract: It is shown that there is a simple separable AF algebra A such that $ M(\mathcal{K} \otimes A)$ does not have weak (FN) and such that the generalized Berg-Weylvon Neumann Theorem does not hold for $ \mathcal{K} \otimes A$.

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  • [Ber] I. D. Berg, An extension of the Weyl-von Neumann Theorem to normal operators, Trans. Amer. Math. Soc. 160 (1971), 365-371. MR 0283610 (44:840)
  • [EL] G. A. Elliott and T. A. Loring, AF embeddings of $ C({T^2})$ with prescribed K-theory, J. Funct. Anal. 103 (1992), 1-25. MR 1144678 (93b:46134)
  • [Lin1] H. Lin, On ideals of multiplier algebras of simple $ AF{C^ \ast }$-algebras, Proc. Amer. Math. Soc. 104 (1988), 239-244. MR 958075 (89j:46065)
  • [Lin2] -, Generalized Weyl-von Neumann theorems, Internat. J. Math. 2 (1991), 725-739. MR 1137095 (92m:46087)
  • [Lin3] -, Approximation by normal elements with finite spectra in $ {C^ \ast }$-algebras of real rank zero, preprint.
  • [Lor1] T. A. Loring, Berg's technique for pseudo-actions with applications to AF embeddings, Canad. J. Math. 43 (1991), 119-157. MR 1108917 (93d:46100)
  • [Lor2] -, Normal elements of $ {C^\ast}$-algebras of real rank zero without finite-spectrum approximants, J. London Math. Soc. (to appear).
  • [MS] J. A Mingo and J. S. Spielberg, The index of normal Fredholm elements of $ {C^\ast}$-algebras, Proc. Amer. Math. Soc. 113 (1991), 187-192. MR 1045144 (91k:46081)
  • [Zha] S. Zhang, $ {K_1}$-groups, quasidiagonality, and interpolation by multiplier projections, Trans. Amer. Math. Soc. 325 (1991), 793-818. MR 998130 (91j:46069)

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