Geodesic
Weakly Stable Relations and Inductive Limits of ${{C}^{*}}$ -algebras
Canadian mathematical bulletin, Tome 46 (2003) no. 4, pp. 588-596

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

We show that if $\mathcal{A}$ is a class of ${{C}^{*}}$ -algebras for which the set of formal relations $\mathcal{R}$ is weakly stable, then $\mathcal{R}$ is weakly stable for the class $B$ that contains $\mathcal{A}$ and all the inductive limits that can be constructed with the ${{C}^{*}}$ -algebras in $\mathcal{A}$ .A set of formal relations $\mathcal{R}$ is said to be weakly stable for a class $\mathcal{C}$ of ${{C}^{*}}$ -algebras if, in any ${{C}^{*}}$ -algebra $A\,\in \,\mathcal{C}$ , close to an approximate representation of the set $\mathcal{R}$ in $A$ there is an exact representation of $\mathcal{R}$ in $A$ .
DOI : 10.4153/CMB-2003-055-4
Mots-clés : 46L05 
Monteiro, Martha Salerno. Weakly Stable Relations and Inductive Limits of ${{C}^{*}}$ -algebras. Canadian mathematical bulletin, Tome 46 (2003) no. 4, pp. 588-596. doi: 10.4153/CMB-2003-055-4
@article{10_4153_CMB_2003_055_4,
     author = {Monteiro, Martha Salerno},
     title = {Weakly {Stable} {Relations} and {Inductive} {Limits} of ${{C}^{*}}$ -algebras},
     journal = {Canadian mathematical bulletin},
     pages = {588--596},
     year = {2003},
     volume = {46},
     number = {4},
     doi = {10.4153/CMB-2003-055-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-055-4/}
}
TY  - JOUR
AU  - Monteiro, Martha Salerno
TI  - Weakly Stable Relations and Inductive Limits of ${{C}^{*}}$ -algebras
JO  - Canadian mathematical bulletin
PY  - 2003
SP  - 588
EP  - 596
VL  - 46
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-055-4/
DO  - 10.4153/CMB-2003-055-4
ID  - 10_4153_CMB_2003_055_4
ER  - 
%0 Journal Article
%A Monteiro, Martha Salerno
%T Weakly Stable Relations and Inductive Limits of ${{C}^{*}}$ -algebras
%J Canadian mathematical bulletin
%D 2003
%P 588-596
%V 46
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-055-4/
%R 10.4153/CMB-2003-055-4
%F 10_4153_CMB_2003_055_4

[1] [1] Blackadar, B., Shape Theory for C*-Algebras. Math. Scand. 56 (1985), 249–275. Google Scholar

[2] [2] Brown, L., Ext of certain free product C*-algebras. J. Operator Theory 6 (1981), 135–141. Google Scholar

[3] [3] Cerri, C., Non-commutative Deformation of C(T2) and K-theory. Internat. J. Math. (5) 8 (1997), 555–571. Google Scholar

[4] [4] Coburn, L. A., The C*-algebra generated by an Isometry. Bull. Amer.Math. Soc. 73 (1967), 722–726. Google Scholar

[5] [5] Cuntz, J., K-Theory for certain C*-algebras. Ann. of Math. 113 (1981), 181–197. Google Scholar

[6] [6] Eilers, S. and Loring, T. A. and Pedersen, G. K., Stability of Anticommutation Relations. An Application of Noncommutative CW complexes. J. Reine Angew.Math. 499 (1998), 101–143. Google Scholar

[7] [7] Friis, P. and Rørdam, M., Almost commuting self-adjoint matrices.a short proof of Huaxin Lin's theorem. J. Reine Angew.Math. 479 (1996), 121–131. Google Scholar

[8] [8] Hadwin, D. W., Closures of direct sums of classes of operators. Proc. Amer.Math. Soc. 121 (1994), 697–701. Google Scholar

[9] [9] Lin, H., Almost commuting selfadjoint matrices and applications. Operator algebras and their applications, Amer.Math. Soc. 13, Fields Inst. Commun., 193–233. Google Scholar

[10] [10] Loring, T. A., C*-Algebras generated by stable relations. J. Funct. Anal. 112 (1993), 159–201. Google Scholar

[11] [11] Loring, T. A., Lifting Solutions to Perturbing Problem in C*-Algebras. Amer.Math. Soc. 81997, Fields Institute Monographs. Google Scholar

[12] [12] Monteiro, M. S.,Weakly Stable Relations and Inductive Limits of C*-algebras. University of New Mexico, July, 2000. Google Scholar

[13] [13] Murphy, G. J., C*-Algebras and Operator Theory. Academic Press, New York, 1990. Google Scholar

[14] [14] Phillips, N. C., Inverse limit of C*-algebras and applications. Operator algebras and applications 1, Cambridge Univ. Press 135, LondonMath. Soc. Lecture Note. Ser. 1988, 127–185. Google Scholar

Cité par Sources :