Approximation of normal elements in the multiplier algebra of an AF -algebra

Authors:
Terry A. Loring and Jack Spielberg

Journal:
Proc. Amer. Math. Soc. **121** (1994), 1173-1175

MSC:
Primary 46L05

DOI:
https://doi.org/10.1090/S0002-9939-1994-1211584-5

MathSciNet review:
1211584

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that there is a simple separable AF algebra A such that does not have weak (FN) and such that the generalized Berg-Weylvon Neumann Theorem does not hold for .

**[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**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*-*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*-*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*-*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*-*algebras*, Proc. Amer. Math. Soc.**113**(1991), 187-192. MR**1045144 (91k:46081)****[Zha]**S. Zhang, -*groups, quasidiagonality, and interpolation by multiplier projections*, Trans. Amer. Math. Soc.**325**(1991), 793-818. MR**998130 (91j:46069)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
46L05

Retrieve articles in all journals with MSC: 46L05

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1211584-5

Article copyright:
© Copyright 1994
American Mathematical Society