Geodesic
REMARKS ON ${\mathcal{Z}}$-STABLE PROJECTIONLESS C*-ALGEBRAS
Glasgow mathematical journal, Tome 58 (2016) no. 2, pp. 273-277

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

It is shown that ${\mathcal{Z}}$-stable projectionless C*-algebras have the property that every element is a limit of products of two nilpotents. This is then used to classify the approximate unitary equivalence classes of positive elements in such C*-algebras using traces. 
ROBERT, LEONEL. REMARKS ON ${\mathcal{Z}}$-STABLE PROJECTIONLESS C*-ALGEBRAS. Glasgow mathematical journal, Tome 58 (2016) no. 2, pp. 273-277. doi: 10.1017/S0017089515000117
@article{10_1017_S0017089515000117,
     author = {ROBERT, LEONEL},
     title = {REMARKS {ON} ${\mathcal{Z}}${-STABLE} {PROJECTIONLESS} {C*-ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {273--277},
     year = {2016},
     volume = {58},
     number = {2},
     doi = {10.1017/S0017089515000117},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000117/}
}
TY  - JOUR
AU  - ROBERT, LEONEL
TI  - REMARKS ON ${\mathcal{Z}}$-STABLE PROJECTIONLESS C*-ALGEBRAS
JO  - Glasgow mathematical journal
PY  - 2016
SP  - 273
EP  - 277
VL  - 58
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000117/
DO  - 10.1017/S0017089515000117
ID  - 10_1017_S0017089515000117
ER  - 
%0 Journal Article
%A ROBERT, LEONEL
%T REMARKS ON ${\mathcal{Z}}$-STABLE PROJECTIONLESS C*-ALGEBRAS
%J Glasgow mathematical journal
%D 2016
%P 273-277
%V 58
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000117/
%R 10.1017/S0017089515000117
%F 10_1017_S0017089515000117

[1] 1.Ara, P., Perera, F. and Toms, A. S., K-theory for operator algebras. Classification of C*-algebras, in Contemporary Mathematics, Aspects of operator algebras and applications, vol. 534 (American Mathematical Society, Providence, RI, 2011), 1–71. Google Scholar

[2] 2.Brown, N. P. and Ciuperca, A., Isomorphism of Hilbert modules over stably finite C*-algebras, J. Funct. Anal., 257 (1) (2009), 332–339. Google Scholar | DOI

[3] 3.Brown, N. P., Perera, F. and Toms, A., The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras, J. Reine Angew. Math. 2008 (621) (2008), 191–211. Google Scholar

[4] 4.Ciuperca, A., Elliott, G. A. and Santiago, L., On inductive limits of type-I C*-algebras with one-dimensional spectrum, Int. Math. Res. Not. IMRN no. 11 (2011), 2577–2615. Google Scholar

[5] 5.Coward, K. T., Elliott, G. A. and Ivanescu, C., The Cuntz semigroup as an invariant for C*-algebras, J. Reine Angew. Math. 2008 (623) (2008), 161–193. Google Scholar | DOI

[6] 6.Elliott, G. A. and Toms, A. S., Regularity properties in the classification program for separable amenable C*-algebras, Bull. Amer. Math. Soc. (N.S.), 45 (2) (2008), 229–245. Google Scholar

[7] 7.Elliott, G. A., Robert, L. and Santiago, L., The cone of lower semicontinuous traces on a C*-algebra, Amer. J. Math. 133 (4) (2011), 969–1005. Google Scholar

[8] 8.Jiang, X. and Su, H., On a simple unital projectionless C*-algebra, Amer. J. Math., 121 (2) (1999), 359–413. Google Scholar

[9] 9.Lin, H., Cuntz semigroups of C*-algebras of stable rank one and projective Hilbert modules, (2010). Google Scholar | arXiv

[10] 10.Kishimoto, A. and Kumjian, A., Simple stably projectionless C*-algebras arising as crossed products, Canad. J. Math., 48 (5) (1996), 980–996. Google Scholar

[11] 11.Nawata, N., Picard groups of certain stably projectionless C*-algebras, J. Lond. Math. Soc., 88 (1) (2013), 161–180. Google Scholar

[12] 12.Robert, L. and Santiago, L., Classification of C*-homomorphisms from C (0,1] to a C*-algebra, J. Funct. Anal., 258 (3) (2010), 869–892. Google Scholar

[13] 13.Rørdam, M., The stable and the real rank of -absorbing C*-algebras, Int. J. Math. 15 (10) (2004), 1065–1084. Google Scholar | DOI

[14] 14.Santiago, L., Reduction of the dimension of nuclear C*-algebras, (2012). Google Scholar | arXiv

[15] 15.Tikuisis, A., Regularity for stably projectionless, simple C*-algebras, J. Funct. Anal., 263 (5) (2012), 1382–1407. Google Scholar

Cité par Sources :