Equivalent Definitions of Infinite Positive Elements in Simple C*-algebras
Canadian mathematical bulletin, Tome 53 (2010) no. 2, pp. 256-262

Voir la notice de l'article provenant de la source Cambridge University Press

We prove the equivalence of three definitions given by different comparison relations for infiniteness of positive elements in simple ${{C}^{*}}$ -algebras.
DOI : 10.4153/CMB-2010-042-x
Mots-clés : 46L99, Infinite positive element, Comparison relation
Fang, Xiaochun; Wang, Lin. Equivalent Definitions of Infinite Positive Elements in Simple C*-algebras. Canadian mathematical bulletin, Tome 53 (2010) no. 2, pp. 256-262. doi: 10.4153/CMB-2010-042-x
@article{10_4153_CMB_2010_042_x,
     author = {Fang, Xiaochun and Wang, Lin},
     title = {Equivalent {Definitions} of {Infinite} {Positive} {Elements} in {Simple} {C*-algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {256--262},
     year = {2010},
     volume = {53},
     number = {2},
     doi = {10.4153/CMB-2010-042-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-042-x/}
}
TY  - JOUR
AU  - Fang, Xiaochun
AU  - Wang, Lin
TI  - Equivalent Definitions of Infinite Positive Elements in Simple C*-algebras
JO  - Canadian mathematical bulletin
PY  - 2010
SP  - 256
EP  - 262
VL  - 53
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-042-x/
DO  - 10.4153/CMB-2010-042-x
ID  - 10_4153_CMB_2010_042_x
ER  - 
%0 Journal Article
%A Fang, Xiaochun
%A Wang, Lin
%T Equivalent Definitions of Infinite Positive Elements in Simple C*-algebras
%J Canadian mathematical bulletin
%D 2010
%P 256-262
%V 53
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-042-x/
%R 10.4153/CMB-2010-042-x
%F 10_4153_CMB_2010_042_x

[1] [1] Blackadar, B., K-theory for operator algebras. Mathematical Sciences Research Institute Publications, 5, Springer-Verlag, New York, 1986. Google Scholar

[2] [2] Blackadar, B. and Cuntz, J., The structure of stable algebraically simple C*-algebras. Amer. J. Math. 104(1982), no. 4, 813–822. doi:10.2307/2374206 Google Scholar

[3] [3] Cuntz, J., Simple C*-algebras generated by isometries. Comm. Math. Phys. 57(1977), no. 2, 173–185. doi:10.1007/BF01625776 Google Scholar

[4] [4] Cuntz, J., The structure of multiplication and addition in simple C*-algebras. Math. Scand. 40(1977), no. 2, 215–233. Google Scholar

[5] [5] Cuntz, J., Dimension functions on simple C*-algebras. Math. Ann. 233(1978), no. 2, 145–153. doi:10.1007/BF01421922 Google Scholar

[6] [6] Cuntz, J., K-theory for certain C*-algebras. Ann. of Math. 113(1981), no. 1, 181–197. doi:10.2307/1971137 Google Scholar

[7] [7] Elliott, G. A. and Fang, X., Simple inductive limits of C*-algebras with building blocks from spheres of odd dimension. In: Operator algebra and operator theory, Contemp. Math., 228, American Mathematical Society, Providence, RI, 1998, pp. 79–86. Google Scholar

[8] [8] Fang, X., The invariant continuous-trace C*-algebras by the actions of compact abelian groups. Chinese Ann. of Math.(B) 19(1998), no. 4, 489–498. Google Scholar

[9] [9] Fang, X., The simplicity and real rank zero property of the inductive limit of continuous trace C*-algebras. Analysis 19(1999), no. 4, 377–389. Google Scholar

[10] [10] Fang, X., Graph C*-algebras and their ideals defined by Cuntz–Krieger family of possibly row-infinite directed graphs. Integral Equations Operator Theory 54(2006), no. 3, 301–316. doi:10.1007/s00020-004-1363-z Google Scholar

[11] [11] Fang, X., The real rank zero property of crossed product. Proc. Amer. Math. Soc. 134(2006), no. 10, 3015–3024. doi:10.1090/S0002-9939-06-08357-2 Google Scholar

[12] [12] Kirchberg, E. and Rørdam, M., Infinite non-simple C*-algebras: absorbing the Cuntz algebra . Adv. Math. 167(2002), no. 2, 195–264. doi:10.1006/aima.2001.2041 Google Scholar

[13] [13] Lin, H., An introduction to the classification of amenable C*-algebras. World Scientific Publishing Co., Inc., River Edge, NJ, 2001. Google Scholar

[14] [14] Lin, H., Classification of simple C*-algebras and higher dimensional noncommutative tori. Ann. of Math. 157(2003), no. 2, 521–544. doi:10.4007/annals.2003.157.521 Google Scholar

[15] [15] Lin, H. and Zhang, S., On infinite simple C*-algebras. J. Funct. Anal. 100(1991), no. 1, 221–231. doi:10.1016/0022-1236(91)90109-I Google Scholar

[16] [16] Pedersen, G. K., C*-algebras and their automorphism groups. London Mathematical Society Monographs, 14, Academic Press, London–New York, 1979. Google Scholar

[17] [17] Rørdam, M., Ideals in the multiplier algebra of a stable C*-algebra. J. Operator Theory 25(1991), no. 2, 283–298. Google Scholar

[18] [18] Rørdam, M., On the structure of simple C*-algebras tensored with a UHF-algebra. II. J. Funct. Anal. 107(1992), no. 2, 255–269. doi:10.1016/0022-1236(92)90106-S Google Scholar

[19] [19] Rørdam, M., A simple C*-algebra with a finite and an infinite projection. Acta Math. 191(2003), no. 1, 109–142. doi:10.1007/BF02392697 Google Scholar

[20] [20] Toms, A. S., On the classification problem for nuclear C*-algebras. Ann. of Math. 167(2008), no. 3, 1029–1044. doi:10.4007/annals.2008.167.1029 Google Scholar

Cité par Sources :